Noun adjunct is one label. However, let's keep things practical. If I said "read", you might think "book". If I said "book", it could either mean "read" or "write" a book.
If we are together and we see the same reality, then we see the book (not a magazine or newspaper). However, we can't see "read" or "write". This makes the verb very important to convey meaning. If you say "read" and only have a book in front of us, I can infer you mean "read the book" with just hearing the word "read". Same could be said of a parent telling their baby to "drink" while holding a baby bottle of milk to their lips. The baby doesn't have to know there is milk inside.
The adjective gives us a second layer to distinguish things. For verbs, we call them adverbs. "ad" in both cases means "in addition to".
With "up", it can be used with verbs or by itself. To "walk up" gives a logical image of someone walking in a straight line (instead of "come" or "go" which could be used instead of run, fly, or ride). To "give up" is harder to imagine, and it's used more to emphasize quitting something because of frustration. If we only used "stop", it wouldn't convey a negative thought.
Is this still confusing for you? That's "up" to you to decide. It's "your call".