All modern languages I know allow expressing essentially the same thing in different ways, and sometimes there is a difference in the level of formality. Formality is not binary; I would not say strictly that one variant is formal and the other is informal, only that one is more formal than the other.
Let me give some examples: In English the contracted forms "didn't" and "I've" are more informal than "did not" and "I have". In Finnish many pronouns (minä, sinä, tämä, tuo, …) have informal variants (mä, sä, tää, toi, …) that are commonly used in speech and online discussions but are not used in printed or broadcast news. In mathematics logical implication symbols and quantifiers (⇔, ∀, …) are often used when solving problems or teaching, but in more formal printed contexts like textbooks or articles they are typically replaced by words (if and only if, for all, …). The point is that the same thing can be expressed in two ways and there is a difference in the level of formality between the two. I want to know if this phenomenon existed in classical Latin.
I am looking for "informal spelling variants" in Latin. With this I mean variant forms of words (or other similar variations) which are more informal than the usual version. I assume that if there is a difference in formality, the most typical variant is more formal; if this assumption is wrong, I would be happy to see "formal spelling variants" as well.
I know that there are spelling variations in Latin, for example perfect syncopation (amavisse > amasse), -ris/-re as a passive ending, and -nl-/-ll- with prefixes ending in -n. However, I am not aware of any difference in the level of formality in these variations. The only thing that comes to my mind is replacing au > ō (eg. Claudius becoming Clodius), but I'm not sure if this really has a formality difference.
I do not mean abbreviations that would also be used in formal occasions, but something more casual (whatever that might mean). Any kind of evidence is fine: inscriptions, contemporary remarks, or other. It does not matter if the sense of informality developed later, although I do prefer formality differences observed during the classical period. Any examples where we have a good reason to suspect informality in some sense would make good answers. If the informal status is uncertain (eg. is Plautus more archaic than colloquial?), examples with the appropriate caveats would be good.
Were there informal spelling variants in classical Latin? That is, were there alternative ways to spell (or perhaps pronounce) words that could be considered informal? If such things exist, I would like to know a couple of words (or short phrases) with two alternative spellings, one of which is more formal than the other. The examples can also be regional (dialect difference), as long as there is a difference in formality; perhaps a spelling variant used in Hispania was considered more informal than the one used in Rome.
(This question went through a complete rewrite. I hope it is less unclear now. Many thanks for C. M. Weimer, brianpck, and Cerberus for the help!)