Tenacity - qualitative description of mineral behavior/fracture under various loads. Tensile strengths - quantitative measure of material strength under tensile load.

http://www.minerals.net/resource/property/Tenacity.aspx

Tenacity = Breaking load / Total denier 

Tensile strength is breaking strength per unit area Kg/mm2

Tensile strength - the resistance of a material to breaking under tension.

Tenacity - Tenacity describes the reaction of a mineral to stress such as crushing, bending, breaking, or tearing. Certain minerals react differently to each type of stress. Since tenacity is composed of several reactions to various stresses, it is possible for a mineral to have more than one type of tenacity. 

Breaking, load normally in newtons, divided by linear density, normally in tex.

You can convert from Tenacity to GPa by dividing by density in g/cc. for a multifilament fiber like a carbon nanotube, the density is hard to measure, so reporting data in Tenacity is more accurate.

I got the answer from this website.

Link: https://www.minerals.net/resource/property/Tenacity.aspx

Tensile strength - the resistance of a material to breaking under tension.

Tenacity - Tenacity describes the reaction of a mineral to stress such as crushing, bending, breaking, or tearing. Certain minerals react differently to each type of stress. Since tenacity is composed of several reactions to various stresses, it is possible for a mineral to have more than one type of tenacity.