Webster's New World Dictionary (1991) informs us that the word is borrowed from French and meant "a pasting," deriving from the French word colle, meaning "paste." It also provides this definition:

collage
1) an art form in which bits of objects, as newspaper, cloth, pressed flowers, etc, are pasted together on a surface in incongruous relationship for their symbolic or suggestive effect
2) a composition so made
3) any collection of seemingly unrelated bits and parts, as in a photomontage.

This brings us to the second term, "montage" — but what is a montage?

According to the same dictionary, this term is also borrowed from French and originally meant "a mounting or setting together," deriving from the French word monter, meaning "mount." And it provides this definition:

montage
1a) the art or process of making a composite picture by bringing together into a single composition a number of different pictures or parts of pictures and arranging these, as by superimposing one on another, so that they form a blended whole while remaining distinct, or
1b) a picture so made
2a) the process of editing film
2b) the art or process of producing a sequence of abruptly alternating scenes or images or a sequence in which superimposted images are shown whirling about, flashing into focus, etc., to convey an idea
2c) a part of a film in which this is used
3a) any similar technique, as in literature or music, of juxtaposing discrete or contrasting elements
3b) anything that is or is like the result of such a process.

From the above, it seems clear that both terms could apply to most of my cut-and-paste paper assemblages, although collage is less precise than montage.

I now work with both 'cut and paste' and 'digital' techniques, so some of my newer pictures would be termed "digital collages" or "digital montages."