Today's examples are brought to you by Star Trek: TOS, Star Trek:TNG, Star Wars, The Lord of the Rings, The Professionals, and The Sentinel. It's like a council of fandoms, counselling us on appropriate word usage.
A definition of council sourced from The Free Dictionary:
1. a. An assembly of persons called together for consultation, deliberation, or discussion.
b. A body of people elected or appointed to serve as administrators, legislators, or advisors.
c. An assembly of church officials and theologians convened for regulating matters of doctrine and discipline.
T'Pau's rejection of a place on the Federation Council inspired both awe and considerable confusion - among humans, at least.
The Jedi High Council was, often as not, riven by factions.
Counsel as defined at the same site:
1. The act of exchanging opinions and ideas; consultation.
2. Advice or guidance, especially as solicited from a knowledgeable person.
3. A plan of action.
4. Private, guarded thoughts or opinions: keep one's own counsel.
5. A lawyer or group of lawyers giving legal advice and especially conducting a case in court.
Deanna Troi's counsel was very sought after on the Enterprise, especially in regard to suppliers of high quality chocolate.
Luke was unimpressed with Han's counsel that a good blaster was more use than an ancient weapon and some hokey religion.
The Online Etymology Dictionary states that people have been confusing council and counsel since the 16th century, so it's a long-standing source of puzzlement. Have some more examples, contrasting the uses in the same sentence:
Elrond long kept his own counsel about some consequences of the Council of Elrond.
After Bodie and Doyle discovered Councillor Webb’s abuse of his position, that gentleman had a very unsatisfactory discussion with his legal counsel.
Blair was a little amused to discover that Simon had been president of his school’s student council, but Jim counselled him that it wouldn’t be wise to tease the Captain about it.
Mnemonics? It may be useful to associate council with the words civic or city; there are shared associations of government, plus those shared 'c's and 'i's.
Counsel has associations with the words consult and support (for example, someone seeking psychological counselling), so remember the 's'.