The use of these phrases varies according to where you are in the English speaking world. So in the UK we use the phrase, "defence counsel" (NB defence with a "c" not "s"). In the USA they use the phrase, "defense attorney". In the USA there are public defenders (and since 2001 in the UK also) - these are lawyers employed by and paid for by the government to defend people who cannot afford their own lawyers. I think the last two are American phrases - the court appointed defense counsel is a lawyer appointed by the court to defend people who can't afford a lawyer. They are paid by the government but not employed by them. I've not heard the phrase, "official defense counsel" so can't help you on that one, though I would suspect it is a general description of all the others.

It is my understanding that all of those names are used to describe the same person. However, I haven’t heard the name”official defence counsel”.