"Initial" Kinetic Energy = Work + "Final" Kinetic Energy
Work = Force x Distance (think of the bullet moving through the animal)
Pressure = Force/Area
Stress is basically the objects resistance to the pressure that it experiences
Materials deform based on the stresses they experience along with the object's geometry, modulus of elasticity, yield strength, ultimate strength, etc. Even though bullet mfg marketing departments refer to "minimum impact velocity", materials do not actually deform based on velocity (the earth spins pretty fast....).
Since velocity is part of kinetic energy, you could somewhat simplify to "minimum impact velocity" IF you were speaking about a single bullet (single caliber, geometry, material composition, etc). The main reason the distinction matters is because marketing refers to a whole bullet line. Would you think it'd be okay if a single BC was given for an entire bullet line? What about a single MV for an entire line of ammo?
You don't even have to run through a complete finite element analysis to see that there will be a standout in any bullet line as well as a poor performer (particularly when you are designing a bullet to perform well in terms of interior, exterior, and terminal ballistics). The differences can get into the double digit percentages. So a bullet that is marketed with a "minimum impact velocity" of 1,600 fps (for example) for the entire bullet line could actually be +/- 1,800 fps (for example) for your caliber/weight of bullet in that line (a difference of about a couple hundred yards). But if you use the standout bullet in that line, you could get all the way down to ,600 fps.
I get the old fudd adage about minimum energy needed to kill, and I get that those statements hit some people in the feels. That's not what I'm talking about at all. I'm speaking to the fundamental facts surrounding the mechanics that describe how, and to what extent, objects deform (bullets expanding in this case).
To go on a tangent, look at those minimum energy 'requirements', correlate them to a typical 30-06 load back in the 60's, and what ranges that would result in. Whether people knew it or not, I think they were applying the wrong term (energy) to what they experienced in the field, which was past _____ yards, it was pretty tough to consistently drop animals with the ammo/rifles/scopes and skill level of the average shooter during that time. And whether people understand it or not now, they are using the wrong term (impact velocity) to describe what's required to cause a bullet to expand......maybe they are just contemporary fudds?