In my humble understanding of the terms

Fracture resistance is the nominal property of a material when this is resisting the development of a fracture and

Fracture toughness is a quantitative way of expressing a material's resistance to fracture when a crack is already present.

please study the Text Book, for example, Philips or Principle Dental Materials.

I will try to answer this question avoiding the use of the exact terms and concepts (which surely is technically convenient, but nobody involved in just biomedical research would understand it). Sorry about that.

In normal life, it is impossible to break a solid body if it is not deformed anyway (say, in compression, traction, torsion, bending, shear). Thus, within a wide extent, resistance to be deformed (stiffness) provides resistance to be broken down (strength).

This looks simple, but in the middle there is a trick (involving just the "toughness" coincept !). The deformation of the body leads to a fracture always acknowledging a a starting point and an end point. The end point is obviously the separation of the body into fragments. The starting point is the induction of some "crack" (discontinuity) into the body's microstructure. The mechanism of fracture involves the growing of that crack and/or the induction of other cracks that finally converge into a single, "critical" crack that completely reaches the external boundaries of the body. Then, the result could be no other than fragmentation.

In general terms, materials can be regarded as "strong" when they offer a relatively high "general" resistance to break, and "weak" in the opposite case. The corresponding properties are technically known as "strength" (please do not confound with "hardness") and "weakness" or "fragility" (please do not confound with "softness").

There exist some kinds of materials that are particularly difficult to deform, but extremely sensitive to the formation of the first crack by just a bit of deformation, and also to the progress of any crack, so that they oppose virtually no resistance to fracture thereafter. Practical examples are marble or glass, or the dry arm of a tree. You can cut a glass sheet extremely easily by just making a small "mark" (the first crack) with some hard element (usually a piece of diamond) on one of its surfaces from one edge of the sheet to the other, and then get it separated into two pieces by just "bending" gently the sheet with your hands. This sort of materials are regarded as "brittle" (please do not confound with "weak" or "fragile").

Opposedly, other materials offer quite a high resistance to be separated into fragments after the formation of the first crack when they are deformed. Practical examples are steel, aluminium, a fresh bone, or the fresh arm of a tree. This kind of materials are regarded as "tough" (please do not confound with "strong") as opposite to "brittle".

Now I think the concept of "toughness" could be easily captured by anhy reader interested in working with mechanical terms despite of ignoring anything technical related to it. In a super-facilitated language, "toughness" would mean "resistance to complete a fracture once the mechanism of its production has started by the formation of a crack".

In particular, all moving bones are levers constituted by a relatively "strong", "stiff" and "tough" material. It may look simple at a first glance, but for Nature it looked to have been quite a hard problem to determine how much to mineralize bone collagen in order to get bone matrix "stiff" enough as to resist the formation of the first crack, avoiding going too far as getting it too much "brittle" as to behave like glass or marble (precisely, the "marble bone" disease ("Schoenberg's disease") offers this pathological instance). The biological answer through Natural Selection was just to achieve the strikingly constant degree of mineralization collagen shows in any vertebrate's moving bones.

Now, let's try to get some of the above concepts together, just to "fix" them into the common reader brain:

    a. Biomechanically speaking, bones need 1. to be stiff enough as to prevent the formation of a first crack under deformation by the usual loads, and 2. to be tough enough as to prevent the formation of all the first and further cracks that could complete the fracture.

    b. A bit more "technically" explained, "bone strength is a combination of bone stiffness (relevent to fracture chiefly at the beginning of the deformation process) and bone toughness (relevent to fracture predominantly later on the deformation process". 

Going just one step further, we can now distinguish between "stiffness" and "toughness" at two different levels of structural complexity, namely, tissue (bone mineralized tissue) and "organ" (the whole bone) levels. When we refer to tissue stiffness or toughness, we are speaking of bone "material" properties. When we refer to whole-bone stiffness or toughness we are speaking of bone "structural" properties.  

Going now a further step on, please believe me (just trust me, I am a scientist !), the whole-bone (structural) properties depend exclusively (yes, I told "exclusively" and also marked it) on bone tissue (material) properties and bone geometrical properties (bone design). No more than that. Readers are kindly invited to forget any "direct" dependence of bone strength upon bone "mass", "density", BMD, T-scores, remodeling, or whatever the commercial panphlets try to insert into their brains. 

Let's go just one further step on? Now every reader should understand me if I say

    1. Bone tissue (material) strength depends on bone tissue (material) stiffness and toughness, and whole-bone (structural) strength depends on whole-bone (structural) stiffness and toughness.

    2. Both (material, structural) these bone "mechanical properties" depend always and only (I repeat, always and only) on "quality" and "distribution" components. Bone tissue stiffness (the so-called "tissue elastic modulus") depends on collagen quality and mineralization, crystallinity, etc (quality) and the spatial disposition of the fibres (micro-structure - distribution) and bone tissue toughness depends on collagen quality again and "sacrificial bonds", anti-creep factors, stress-raisers as pores, lacunae, canaliculi, cracks, etc (quality) and their density or ortientation (distribution). Whole-bone stiffness depends on bone material stiffness (quality) and cortical or trabecular design (distribution). On time, the whole-bone design can be classified into cortical shell design (quite well defined by cortical diameters, thickness, buckling ratio and cross-sectional moments of inertia) and trabecular network design (the wrongly-called "bone micro-architecture", which is rather poorly defined by the known parameters assessed by HMM or uCT and other things).

Let's dare to propose now (going to extremely simplified concepts) that

1. Whole-bone (structural) strength depends on whole-bone (structural) stiffness and whole-bone (structural) toughness.

2. Whole-bone (structural) stiffness depends on bone tissue (material) stiffness and (cortical or trabecular) bone design.

3. Whole-bone (structural) toughness depends on bone tissue (material) toughness and (cortical or trabecular) bone design.

4. Both bone tissue (material) stiffness and toughness depend on molecular components including collagen fibers and their spatial distribution (micro-structure)

5. Please distinguish between the three "bone qualities": a. bone "material or tissue" quality, b. bone "geometric, architectural of design" quality, and "whole-bone" (structural) quality. Only the latter is a synonymus of bone strength, or bone resistance to fracture, which is the important propertiy for clinicians and epidemiologists. When a physician speaks on "bone quality" he must explain (we hope he/she is able to!) to what kind of "quality" he/she is making reference.

From "2,3,4" above we deduct that everything in bone biomechanics is a matter of "quality" (material properties) and "distribution" (geometric properties, design).

Corollary. Not too striking as it looks. Think about, everthing in life (drinking a glass of wine, selecting the fiancee, allowing the kids going outside, complain against taxes, vote for a candidate, earning money, eating, breathing, living, reading silly writings like this one, etc) is a matter of quality and distribution.

Sorry again, I am totally unable to teach all the above any easier (Engineers please keep silence).

You can use single test type, according ASTM standard, monotonic loading of precracked specimen. If your material specimen experienced unstable failure, you can calculate the material fracture touhgness from the load and the crack length. In case of stable crack openning, you calculate J integral from mwechanical energy and crack lengths as fracture resistance characteristics. The two values have different meaning (stress intensity resp. energy for crack advance) and cannot be simply recalculated one to another.

Yes, I agree with your first part. It is better to separate the definitions.

Fracture toughness is a material characteristics meaning its resistance against a crack propagation.

If the material is brittle or low toughness, the fracture toughness is determined as a critical value of stress intensity factor at failure.

If the material is high toughness, the fracture toughness is determined as a normalized critical value of J integral (energy based) at the onset of the crack extension. The J integral is sometimes called resistance because J versus crack extension curve is called the resistance curve.