This answers pertains to the United States, not Great Britain, nor perhaps Canada.
"Attorney" and "Lawyer" are, for most purposes, synonyms.
For questions of this nature, which involve some specialization and may involve jargon (in this case legal jargon or usage) one should consult a good specialist dictionary. An excellent source for this is Black's Law Dictionary (or Ballantine's). "Lawyer" is defined in Black's as follows:
"a person learned in the law; as an attorney, counsel or solicitor; a
person who is practicing law."
The reason I say "for most purposes" is that as a non-lawyer I may be appointed to be your attorney (i.e. given "power of attorney") to act in some or all matters pertaining to you, but I may not practice law, or hold myself out to the public to practice law. To do this I would need to be an "Attorney at Law" or a "Lawyer".
As to the prepositional phrase "at Law", the basic law of the United States remains English Common Law, especially as it existed at the time of the Revolution. The prepositional phrases "at law" or "in law" hark back to this. The only state of the Union which does not have Common Law as its basic law is Louisiana, which due to its origins as a French colony retains a form of Roman Civil Law. See Wikipedia.
By "basic law" I mean "law of the land". It is the law that exists even if all statutes were to be repealed. Most provisions of common law have been replaced by statute law, but it is still possible on occasion to revert to the common law. An old acquaintance of mine who was a highly-knowledgeable non-lawyer one time managed to convince a judge that a particular statute did not apply in a case, and the court proceeded to treat the case as an "in Law proceeding", i.e. that the Common Law would govern. Anyway, anytime you hear the phrases "at law" or "in law" it is the Common Law that is meant. Usually, anyway.
Incidentally, some people have the idea that the Common Law does not exist any longer in the United States, but this is false. Most states explicitly state in their statutes that the Common Law is still in effect. This example from Washington State's "Revised Code of Washington" should suffice to persuade that this is the case.
RCW 4.04.010 Extent to which common law prevails.
The common law, so far as it is not inconsistent with the Constitution
and laws of the United States, or of the state of Washington nor
incompatible with the institutions and condition of society in this
state, shall be the rule of decision in all the courts of this state.