Virginia once had a House of Burgesses. Now we have a lower house of Delegates and an upper house of Senators.
The US federal system has senators as well, with a lower house of Representatives.
Some cities have aldermen. Or council members. The UK has a parliament.
Council members
Alderman
Burgesses
Members of Parliament
Senators
Representatives
What am I missing? What other terms have been used for deliberative bodies in the English-speaking world?
Some northern states have SELECTMAN, similar to a council member.
Oh, just remembered;
The San Francisco Board of Supervisors is the legislative body within the government of the City and County of San Francisco, California, United States.
Well, in the U.S., Senators and Representatives together are known as Congress.
Board
Elders (presbyterium in ecclesiastical talk)
Freeholders
Diet
And now… to the thesaurus…
assembly
association
caucus
chamber
club
(executive) committee
conclave
conference
convention
convocation
forum
guild
league
legislature
symposium
The House of Lords includes Lords Temporal and Lords Spiritual.
The Continental Congress was made up of delegates.
New York has an Assembly and a Senate. Additionally, many counties in New York have legislative chambers which are just called Legislatures. (Not very creative.) The members are called Legislators.
Some towns have boards of Selectmen or Supervisors.
City Council
Town Council
Legislative Assembly
Legislative Council
House of Assembly
House of Delegates
National Assembly
National Council
Nebraska has a “Unicameral”.
The Nebraska Legislature is called the Nebraska Legislature. Unicameral is an adjective and just means it has one chamber.
What do they call the leaders in communist countries? Are there any secular councils in the middle east? what are their members called?
I’m especially curious what our Asian friends call their senator-types, though I’ve got this vague impression (possibly mistaken) that most of Asia is either communist (China, N. Korea, Vietnam) or still using a monarchical system with hereditary (rather than elected) nobility.
You know only the top half of Korea is communist, right? 
The South Korean legislature is called the National Assembly in English. Japan of course has its famous bicameral Diet, with the senior house being a House of Councillors.
Perhaps officially, but I have heard Nebraskans refer to their state legislative body as ‘The Unicameral.’
Yeah, well Nebraskans also make sculptures out of butter so don’t take anything they say too seriously.
“Diet” etymology?
With the permission of OP, may this be opened to non- Anglo, as long as literals or root concepts are explained?
Eg, the parliamentary body in Israel is the Knesset (although no caps in Hebrew).
From to come together (kns trilitteral root). Actually that’s probably wrong. Passive noun “have been gathered”? I must leave it to people who know more.
Anyway, that sort of post.
Also, a governing body of the Soviet Uniin is…a Soviet. But I don’t know what that means literally.
Also, for English, I just found that the Confederate States of America remains a functioning government-in-internal-exile (does the FBI know about this?!! More important, does Ken Burns?) and they refer to their legislators as “representatives.”
The “lower” half of the Mexican national legislature (the equivalent of the House of Representatives) is the Chamber of Deputies.
The upper half is, of course, the Sheriffs.
Original Spanish for each?
Let me introduce you to a multisearching online dictionary: OneLook.
Among the dictionaries results, I recommend going to the American Heritage Dictionary of the English Language, which is the one Yahoo uses, for etymologies. Your answer is here: Yahoo | Mail, Weather, Search, Politics, News, Finance, Sports & Videos
Is there something you’d like me go Google for you or look up on Wikipedia? 
The single (unicameral) chamber is called the Senate.