These are more slang words, so it is not appropriate to compare them to informal and formal speech patterns. In English we tend to use formal words in written form or in serious situations, whilst informal speech tends to use lots of contractions such as 'he's' instead of 'he has'.

I agree with what Jacob said about lazy texters using slang and extreme contractions which cannot be spoken themselves.

We do, however, have many different youth sub-cultures who develop their own style of language and these words do sometimes become mainstream and perhaps even end up officially in the dictionary. I think that these are the kind of word you are referring to.

While I agree we have different formallity levels, English doesn't use different words to express this. In the example of "Cuz and Because" The first one is never spoken,and only typed by lazy texters xD Texting slang such as: cuz, lol, ttyl, u, and r u are not really part of our formallity levels. Also "Gonna" is not a formallity level but part of a dialect. In the southern USA people talk using such words all the time, and it is comon place even in formal situations. "Chill and Relax" have two different, but very close, meanings.

I hope I helped! ^ ^