A few years ago while walking near an Applebee's I couldn't help to notice there was something familiar about the logo. When I compared the two I realized that both Applebee's & Mar Y Sol have the same font.

So, who came first?

Mar Y Sol was first.

Applebee's was founded 8 years after (1980).

What else do they have in common?

Mar Y Sol was created by a very well known music promoter, Alex Cooley, from Atlanta, Georgia.
Applebee's was also founded in Atlanta, Georgia.

As of now I have no further details about any relation between Cooley and the founders of Applebee's.