What term includes words and parts of words?

It depends on whether the word chunk is a meaningful constituent or not. Most chunks aren't.

In international, there are at least three Morphemes -- maybe four, depending on whether one counts the in- in inter:

• in-ter . nation . al

Morphemes are the meaningful chunks of words, like book and keep in bookkeepers, as well as derivational and inflectional bound forms like -al, -er, and -s.

However, meaningless substrings such as terna, ookkee, or nal are not morphemes.