I've done it several ways.
Sometimes I match them. Othertimes I have a patterned cloth and solid napkins or a solid cloth with patterned napkins. And then sometimes I have a solid cloth with contrasting solid napkins.

It depends on the other things I have on the table, such as pitchers, bread baskets, casserole, etc. Sometimes my table needs a little extra color and sometimes I just like a more elegant simple look.

"In a formal dining room with a cloth tablecloth, should the cloth napkins be an exact match to the tablecloth or can/should they be different?"

By 'formal' do you really mean 'formal'?

If you are doing a white tie affair they should match. Otherwise you can mix it up. Things are much more casual nowdays.

Ditto Dilly Dally.
Gosh I seem to always agree with you! You must be a very smart woman to think like me.

I never do matchey matchey. Even if I were setting a table for a state dinner at the White House, but that's me.

....Jane