To clarify, I'm referring to the terminology for the difference between just a the word "see" as a verb, and the word in a statement like "Alice sees Bob". What is the correct terminology for the latter statement?
There's no terminology that generically describes all such differences, but the most likely kind of difference, what I suppose you have in mind, relates to the idea of a "verb form" – under that heading you would include for instance "saw", "seeing", "seen". In English, verbs can have a number of forms depending on syntactic properties ("the subject is third person singular") or semantic properties ("happened in the past"). English is somewhat special in that there are forms that don't add anything to the bare verb root ("cook", "carry" etc.) and those forms are used in a myriad of contexts, but other forms add something ("cook-ed, cook-s, cook-ing") so that you get e.g. the "past tense" form and so on. So you could talk of forms like "see, cook" as the uninflected form, or the basic or bare form. Usually we call "cook" et al. the uninflected form. It's not wrong to call such a form the bare verb; it's a bit unclear to call it the basic form.