can someone explain the different types of Pots

[saxcop2]

I need to replace the bridge volume pot on my Michael Kelly Hex Delux. It has passive pots. It has humbuckers

 

The bridge pup quit working. I thought it might have a bad solder. I resoldered it and it worked but only why the pot was still warm from the iron.

 

I went through this several times and each time it would work until it cooled off.

anyway this has really small pots and its suppose to be a top of the line from MK.

 

I figure I may as well put an coil tap in. I like to be able to roll off my volume a little and bring it up for lead work as a boost.

 

so what is it called that I need and do the shafts come in standard size?