This is what I think of while I'm at work.

The skeleton language is divided into four main groups:

Serif

Script

Blackletter

Dingbat

The most prevalent is Serif, so much so that it has two additional dialects: Slab-Serif and Sans-Serif. 

To someone outside of the language, they would all sound the same. But, to Serif speakers, it's the same difference as UK English vs. American English vs. Australian English. Technically it's all the same language, but there's nuances and slang and vocabulary that are different from each other.

Script is the second most common language. While it shares the same alphabet, it is a completely different language structure. Think English vs. French.

Blackletter is an old language and not much in use--it was basically a proto-Serif. It's comparable to the pockets of people speaking Cornish or Irish or Welsh in the UK.

Dingbat is technical name for the Gaster family's language. No one knows how or why it started, but it needed its own classification because it was completely different. If Serif vs. Script is comparable to English vs. French, then Serif vs. Dingbat is the same as English vs. Russian Sign Language. 

Arial is the communal language of skeletons, derived from bits and pieces of various Serifs and Script, and even a bit of Blackletter. 

(Really, if we're going full-on linguistics, Arial is closer to the development of English, since it's the same hodge-podge of various languages. But it's easier to compare Serif to English rather than saying: "So Serif is Germanic and Script is Gallic and Blackletter is Latin and if you put them together you get Arial, which is like English").

Also, for the hell of it (and because it might be relevant soon), names.

Sans is a VERY common name for male skeletons. It's sort of like "James" or "John"--everyone in the village knows at least one Sans. 

(I also totally stole that headcanon from A Year Every Minute, which is GOOD and you should READ IT.)

Lucida is also a very common female skeleton name. It's like Elizabeth or Sarah, you know at least one.

Papyrus, on the other hand, is a very rare, old-fashioned, dignified name. It, like Palatino, is a name on par with Theodore or Reginald. You may occasionally hear the name, and when you do you hold back a giggle because how fancy.

You will not meet another Wing Ding. Wing Ding Gaster does not know another Wing Ding. His grandfather was apparently named Wing Ding, but he never met him. 

(In the end, none of this matters because the skeleton bros were named as jokes and also possibly as a reference to the comic Helvetica, by j.n. wiedle)

(Yes, I'm busy writing a chapter. I just had to get this out of my head.)