"Postfix" or "suffix"?

I think both can be used interchangeably, although the context sometimes determines which word you are more likely to use. For example, in linguistics, an affix after the stem of the word is called a suffix. In computer programming, when an operator appears after the operand, it is known as a postfix operator.

As far as a file extension goes, my intuition would be to go with "suffix", but I believe that "postfix" would be equally valid.

The word "suffix" has been around since 1778. I was unable to uncover a similar etymology for the word "postfix", leading me to guess that it is a modern invention, as "post-x" is a more obvious candidate for being the opposite to "pre-x". In this regard it is very much like prepone in Indian English, except that it has caught on globally.

From a "pure" English standpoint, postfix is essentially a lesser-used synonym for suffix, both in the noun and verb sense (with the verb being the act of adding a suffix). In fact, my dead-tree American Heritage Dictionary, 2nd College Ed. gives these (and only these) definitions of postfix:

n. A suffix.

tr v. To suffix.

More modern definitions of postfix have cropped up, including the adjective used in computing and mathematics, and a medical verb.

I disagree with Roaring Fish's analysis of the n-grams. I believe postfix and suffix are both rising in large part because of their use in computing. Computer programmers typically use postfix only as an adjective and suffix only as a noun. Therefore, the thing that comes after a dot in the name of a file would only be referred to as a suffix (given just these two choices). The use of suffix dwarfs that of postfix even in computing because plenty more people are exposed to file extensions than to mathematical or programming notation.

Finally, I would like to say that for your particular use (denoting the part or parts of a file name following a dot), extension is actually the most common and preferred term. Normally it refers only to the stuff after the last dot, so if you want to specify the collection of extensions, the most clear alternative is to say just that, or something to its effect. (Other possibilities might be stack, string, or series of extensions.)

In linguistics, the term "postfix" is not so widespread in Anglophone linguistics, the more common one being "suffix".

Indeed, there is a difference between a suffix and a postfix. A postfix is whatever comes after the base of a word, be it a suffix or an ending or even an enclitic. Thus, under this interpretation, a postfix is a hyper(o)nym, whereas a suffix is a hyponym.

The term "postfix" is somewhat more common in German and Russian linguistics, cf. Hall 2000: