Is there a difference between the end state of a Turing machine and the halt state? Especially, for example the Busy Beaver 3. It is said that it is with 3 states but there is also a halt. Is the end state $q_2$ or the $halt$?
"End(ing) state" and "halt(ing) state" are just two (four) different ways of saying the same thing.
In the specific case of the Busy Beaver , the end state is the halt state, al other states (q0,q1,q2) must have a transition defined for every symbol in the alphabet of the TM so the machine doesn't halt on them.