I'm sorry for this, as I know there are already many questions on here concerning inelastic collisions already, but I believe this one is actually slightly different. Although [this][1] has indeed the best response so far! Just wanted to say that.

I (hope at least) understand why kinetic energy is not conserved in inelastic collisions, that is not my issue here. I also believe I understand why conservation of momentum is true in both cases. I am confused about the following though:

Conservation of energy doesn't work, because some of the energy gets converted to deformation / binding energy. Conservation of momentum works, because momentum is, of course, conserved, while some of the energy goes to deformation and binding. Now, this energy which is "lost" to binding and deformation, doesn't that depend on the material and the sort of binding happening? For example, if a bullet lodges into a block of wood, woodn't (see what I did there?) that take more deformation energy than 2 sticky objects sticking together after the one hits the other or if the bullet came twice as far into the block because it was of a softer material?  

So how how does the $m_a*v_a=m_b*v_b$ equation know, how much energy was lost to accomodate for the different binding or deformation energies required for different materials?

The only thing I could think of, is to assume that the entire original kinetic energy remains as kinetic energy in the result system, which it of course does not.

So why is the amount of energy "lost" to other stuff constant for each final energy value? If a block of glue hits another block of glue, the deformation and binding energy is not the same as a bullet hitting a block of wood at the same speed, is it?

(Yes, I know energy is not lost, thus the double quotes)


EDIT: Example:
Say you have a bullet waying $m_a = 0.5kg$ hit a block of wood waying $m_b = 5kg$. After the collision, the bullet is stuck into the block and the total thing has a $E_{kin}=10J$. Now find the bullet's speed.
The solution should be this:  
$m_a * v_a = m_b * v_b | / m_a$  
$v_a = \frac{m_b * v_b}{m_a}$  
so now you do  
$v_b = \sqrt{\frac{E_{kin}}{0.5m_b}}=\sqrt{\frac{10J}{0.5 * 5kg}}=\sqrt{4\frac{m^2}{s^2}}=2\frac{m}{s}$  
which means that  
$v_a=\frac{m_b*v_b}{m_a}=\frac{5kg*2\frac{m}{s}}{0.5kg}=20\frac{m}{s}$  
This calculation makes sense to me: The momentum is conserved and some energy is lost. But if I now calculate the kinetic energy of the bullet:
$E_{kinbullet}=0.5m_av_a^2=0.5*0.5kg*(20\frac{m}{s})^2=100J$  
This energy loss I also understand, the energy goes towards reshaping, heating and so on the block of wood.  
What confuses me is, that the amount of energy which goes towards reshaping and heating and so on is the same for every material. If the block were made of rubber for example (not elastic rubber, the more sticky kind), it would also loose 90J of energy to the rubber. How is that?

Yes, I know this is asked quite commonly, but I had to. I couldn't find any good explanation unfortunately :(

  [1]: https://physics.stackexchange.com/q/466744/