How to tell what is in one vector and not another?

you can use the setdiff() (set difference) function:

> setdiff(x, y)
[1] 1

Yes. For vectors you can simply use the %in% operator or is.element() function.

> x[!(x %in% y)]
1

For a matrix, there are many difference approaches. merge() is probably the most straight forward. I suggest looking at this question for that scenario.