Was Mel's really a diner, or was it a cafe?

it was Mel's Diner

In the movie it was called "Mel and Ruby's Cafe" and also in the pilot episode.

What is the difference in a cafe and a diner anyway?

I did not know in The Movie it was call Mel and Ruby Cafe.

Yes.
In the movie Mel was widowed and he and his late wife owned the diner/cafe.

Alice remarks that the place killed Mel's wife.

But is there a difference in a cafe and a diner? Just curious.

Cafe is a broad term for any small restaurant. Diner was originally a type of structure. But many small restaurant are similar inside and are called diners.

A larger one like Denny's, IHOP, or a motel cafe would be termed "coffee shop." But you could call it any of the three.