Lawyer: anyone whose work mainly consists of legal advice / legal argumentation and who is professionally qualified to do that work across a broad range of different areas of law. In England, "lawyer" is sometimes used to mean "solicitor" (a more specific type of lawyer), but is sometimes used in a broad sense to include academic lawyers who are not professionally qualified, and even law students.
Attorney: has various meanings but can be the professional title of the main kind of lawyer practising in the USA. In England, I believe a "power of attorney" is a document giving you the legal right to make certain kinds of decisions for another person, as their agent ("attorney" meaning something like "legal agent"). In British politics, the Attorney General is the title of a specific political officer-holder who is also a lawyer for the Government. I believe that historically, "attorney" was a title for a particular kind of lawyer in England.
Counsellor: used as a term of address when speaking to a lawyer in a formal context in the American system - the judge might address a lawyer as "counsellor" instead of using the lawyer's name when talking to that lawyer. In England, a "counsellor" is usually not a lawyer but instead a psychological counsellor. In the American school system, a "counsellor" could be a guidance counsellor for students (again, not a lawyer). Compare the word "counsel" which can be a synonym for "barrister" in the English legal system (a specific type of lawyer, different to a solicitor), or for someone performing a role similar to the traditional role of barristers. "In-house counsel" means "in-house lawyer". "General counsel" means the general legal adviser of a company. "Counsel" / "of counsel" may also refer to the level of a particular lawyer within the hierarchy of a law firm (a senior level with similar prestige to a partner).
Practitioner: anyone who works in a particular professional field, not necessarily law (depends on context).