What is the difference between EL34 A,B,C, or PH tubes.

EL34 (A,B, etc) are power pentodes that can also be run in triode mode

Best current EL34 variant is the Gold Lion KT77 by a large margin in my opinion and others whose ears I trust.

I did not even know that there are different types of EL 34 tubes.  A good friend brought over to my place various quads of vintage EL 34 and 6CA7 (1950s and 1960s) tubes.  I got to pick out which quad to keep as a gift to use in my BHSE.  I chose a quad of Telefunken tubes.

You can use any type of EL34 !
https://tubedepot.com/products/sino-el34-b-power-vacuum-tube

I'm not 100% on this but I believe the EL34A is a tetrode and the EL34B is a pentode (like standard EL34) The A and B additions are for new Chinese production, possible for EL34 name copyright)
I'd stick with EL34 and EL34B for your BHSE.