They are very different:
- A rebase is a "magical" operation that modifies branches to update them.
- A cherry-pick by contrast is a fine-grained operation which copies commits.
In fact, cherry picks can even be used to replace rebases.
The outdated branch problem:
An outdated branch is a daily scenario.
- You branched of from a "master" branch,
- Committed some changes,
- While in parallel also the initial "master" branch changed.

As illustrated above, there are several ways to depict this initial state:
- Even though we do tend to show a kind of "branched" diagram when several branches have the same commits. In reality each branch has its own line of commits, some of which have the same hash code.
- It's important to realize that there isn't such a thing as "master" or "child" relation between branches in git. All of that is just orchestrated by naming conventions.
On top of that, usually you would have 2 versions of most branches: a local and remote version. So, if we want to be as verbose as possible, we would show it as follows:
A--B--D (remote) origin/master
A--B--C--E (remote) origin/feature/foo
A--B--C--E (local) feature/foo
The challenge now, is to update the history of our 2 feature branches, to add the missing changes of commit D. And there are in fact 2 ways to accomplish this.
Rebase solution
Rebase really is a magical command that updates a feature branch for you. It does so by adding the missing commits (i.e. commit D of the master) to a branch that "runs behind" a couple of commits. And it does so by adding the commits IN FRONT of the new commits.

After a rebase, all we need to do, is push the result, to update the remote branch with the updated version.
A--B--D (remote) origin/master
A--B--D--C--E (remote) origin/feature/foo
A--B--D--C--E (local) feature/foo
Or as it would often be visualized.

And that kind of gives the impression that our feature branch "moved", while in reality, it just got a bit longer.
Cherry-pick solution
You can in fact accomplish the same by combining a "hard reset" with multiple "cherry-picks". Let's start from the same problem, and perform a "manual rebase" by using cherry-picks.

Which would have the same result as a rebase
A--B--D master
\
C--E feature/foo