Bioconcentration factor (BCF) can be expressed as the ratio of the concentration of a chemical in an organism to the concentration of the chemical in the surrounding environment. BCF is expressed in units of liter per kilogram (ratio of mg of chemical per kg of organism to mg of chemical per liter of water).

National Bioaccumulation Factors - EPA

https://www.epa.gov/sites/production/files/2016-01/documents/national-bioaccumulation-factors-supplemental-information.pdf

Article Bioaccumulation Factors (BAFs) and Biota to Sediment Accumul...

BAF=Cshoot/Csoil; Cshoot and Csoil are metals concentration in the plant shoot (mg/kg-1) and soil (mg/kg-1), respectively. BAF was categorized further as hyperaccumulators, accumulator and excluder to those samples which accumulated metals>1 mg/ kg-1, and < 1, respectively

Find herewith some references for quick review of ur answer.

In general bioconcentration factor applies to uptake in aquatic organisms to uptake directly from water across the gills.  Bioaccumulation includes uptake from water as well as from diet.  For plants the distinction is not really relevant.  In your case BAF/BCF is simply concentration in plant divided by concentration in medium.

1- Bioaccumulation refers to the accumulation of substances, such as pesticides, or other chemicals in an organism. Bioaccumulation occurs when an organism absorbs a toxic substance at a rate faster than that at which the substance is lost.

2-Bioconcentration is a term that was created for use in the field of aquatic toxicology. Bioconcentration can also be defined as the process by which a chemical concentration in an aquatic organism exceeds that in water as a result of exposure to a waterborne chemical.

Above general definition by Wikipedia 

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My opinion is that Bioaacumulation in waste water and plants for example refer to the root which could uptake heavy metals in waste water fields and Bioconcentration in waste water refer to the measure of toxic in area of root. It means that first we need to measure Bioaccumulation  in waste waster in present of plant then Bioconcentration test to know how much toxic absorb with root or others segments of plant.

In my opinion there is a difference between both concepts:

-Bioconcentration reflects a greater concentration of substances in biota as a result of biological processes. As an example, the concentration of C is greater in biota than in water or air, but the bioconcentration factor remains more o less constant in time. It is related with homeostatic control mechanisms.

-Bioaccumulation is the result of a progressive increase of concentration of a substance in a organism and the bioconcentration factor  changes (usually increases) in time and can result in the presence of toxic levels.

I would wager that bioaccumulation is the better one to use. When we think of aquatic plants absorbing a toxicant, it would have to be directly from the water into the tissue somehow (this is because BCF=tissue concentration/water concentration). But when we are specifically referring to metals, at neutral pH most would be water insoluble. Therefore for the plant to take them up is would likely be from the soil that the metals are adsorbed to. Uptake of a toxicant from soil is representative of bioaccumulation. 

Additionally when we talk about bioconcentration from water, we typically incorporate toxicant bioavailabilities, which involve models which require an organism to have gills.

Lastly, it really depends on if you want to look at net accumulation of contaminant or just from water. Bioaccumulation includes bioconcentration, as well as accumulation from air, soil, diet. It also really depends on if you're look at emergent of submergent macrophytes.

Sorry for not providing references

Different organs of aquatic plants (roots, stems, leaves) are able to uptake and accumulate substances from water in varying degrees. This differents can be quantified by the bioconcentration factor. Bioaccumulation factor is useful for the characterization of the substance accumulation by the whole plant.

Both of the the BCF and BAF metrics are: 

concentration(biota) / concentration(respiratory medium, e.g. water)

For animals, the BCF is calculated in a lab-based setting (e.g. OECD 305 guideline for testing with fish) generally through an aqueous-only exposure test. Therefore, the BCF only considers uptake through the respiratory medium. A steady-state BCF can be described kinetically as k1/kT, where k1 is the first order uptake rate constant through respiration, and kT is the first order total elimination rate constant from the body.

On the other hand, the BAF for animals is a field-based measurement, and therefore considers both the repiratory medium and diet as major uptake pathways. As such, dietary magnification of chemicals is also possible through the BAF, and chemical "fugacities" or "activities" can actually be greater in the organism compared to in the water. A more appropriate metric to evaluate for bioaccumulation. 

For plants, I believe these two metrics could be used interchangeably, since uptake is passive and only through the respiratory medium. However, it could be argued that the BCFplant measurement is done in a lab-based setting and a BAFplant from the field. 

To normalize data between experiments, the BCF or BAF are often normalized to a lipid basis (e.g. for fish a 5% lipid weight).

http://www.oecd-ilibrary.org/environment/test-no-305-bioaccumulation-in-fish-aqueous-and-dietary-exposure_9789264185296-en

Article A review of bioconcentration factor (BCF) and bioaccumulatio...

I think this paper can be help for this question:

Jon A Arnot, Frank APC Gobas. 2006, A review of bioconcentration factor (BCF) and bioaccumulation factor (BAF) assessments for organic chemicals in aquatic organismsEnvironmental Reviews, Vol. 14, No. 4 : pp. 257-297. https://doi.org/10.1139/a06-005

Thanks a lot Ilker Ugulu. It is useful paper.

Thank you, too. You ask a good question. I have benefited from the replies too. Greetings.

Bioconcentration factor (BCF) can be expressed as the ratio of the concentration of a chemical in an organism to the concentration of the chemical in the surrounding environment. BCF is expressed in units of liter per kilogram (ratio of mg of chemical per kg of organism to mg of chemical per liter of water).

National Bioaccumulation Factors - EPA

https://www.epa.gov/sites/production/files/2016-01/documents/national-bioaccumulation-factors-supplemental-information.pdf

Article Bioaccumulation Factors (BAFs) and Biota to Sediment Accumul...

BAF=Cshoot/Csoil; Cshoot and Csoil are metals concentration in the plant shoot (mg/kg-1) and soil (mg/kg-1), respectively. BAF was categorized further as hyperaccumulators, accumulator and excluder to those samples which accumulated metals>1 mg/ kg-1, and < 1, respectively

Dear Hameed, I am in a fit matching answer of this question with my colleagues Dr. Boris and Dr. Monica for Bioconcentration and Bioaccumulation Factors.

Best regards,

Naseer Almukhtar

The difference between BCF and BAF may after all be a matter of semantics.

It is just semantic because both are computed the same way and mean the same thing.

In the case of soils and plants, it seems necesary to me, to choose which part of the plant to put in the denominator so that be comparable. Is it just shoots or is it the whole plant or is it shoots/roots? and off course to use same methods.

When calculating bioaccumulation factor, BAF=Cshoot/Csoil, Which of the following concentrations best to consider as Csoil, Total soil concentration or Bioavailable concentration?

If you want to built a model or explain the observations, I would prefer to use the bioavailable concentration, provided that this is determined with a proven - preferable validated - method.

Bioconcentration factor (BCF) is the ratio of the concentration of the substance in a specific genus to the exposure concentration, at equilibrium (Paradigms Lost, 2006 )

Bioaccumulation factor is defined as the ratio of metal concentration in plant biomass to that in the soil, and translocation factor is defined as the ratio of metal concentration in the shoots to that in the roots .

Have a look at these papers:

Phytoremediation of Red Mud Deposits Through Natural Succession

Tripti Mishra, Vimal Chandra Pandey, in Phytomanagement of Polluted Sites, 2019

Chemical Partitioning and Transport in the Environment

Brian L. Murphy, in Introduction to Environmental Forensics (Third Edition), 2015

Is the bioconcentration factor same as the transfer factor?

Monika Lal Bioconcentration factor is different as translocation Factor,

BCF= Conc Metal in plant biomass/Conc Metal in Soil

TF=Conc Metal in Shoots/Conc Metal in Roots

The only issue that I see is that some researchers present the plant biomass as shoots, or roots or complete plant, so care must be taken when comparing each other data. Or I am getting something wronge?

That is absolutely correct Beatriz Amanda Watts and if the metal concentration could be replaced with the contaminants, the BCF formula works fine.