Will remote URL for fetch and push be different?

Yes (using different remote), and that is why Git 2.5 introduces a new ref shorthand @{push}.
See "Viewing Unpushed Git Commits"

What commands can you use to change remote URL for fetch or push separately?

You need a separate remote:

git remote add myfork /url/for/my/forkgit config remote.pushdefault myfork

The GitHub blog post "Improved support for triangular workflows" illustrates the use of @{push}:

See what commits you've added to your current branch since the last push:

git clone https://github.com/YOUR-USERNAME/atomcd atomgit config remote.pushdefault origingit config push.default current

• remote.pushdefault specifies where to push (to which remote repo).
• push.default specifies what to push (what refspec), when no refspec is explicitly given.
  current, in that latter case, means "push the current branch to update a branch with the same name on the receiving end."

The following branch will fetch from one url, push to another:

git remote add upstream https://github.com/atom/atomgit fetch upstreamgit checkout -b whizbang upstream/master

(Here the whizbang branches tracks upstream/master, but pushes to origin/whizbang)

git log @{push}..

This uses the new @{push} notation, which denotes the current value of the remote-tracking branch that the current branch would be pushed to by git push, namely origin/whizbang.
You can also refer to the push destination of an arbitrary branch using the notation whizbang@{push}.

From documentation, Fetch and Push URLs should be same.

http://git-scm.com/docs/git-remote

Command to set Push and fetch urls

'git remote set-url' [--push] <name> <newurl> [<oldurl>]

Note that the push URL and the fetch URL, even though they can be set differently, must still refer to the same place. What you pushed to the push URL should be what you would see if you immediately fetched from the fetch URL. If you are trying to fetch from one place (e.g. your upstream) and push to another (e.g. your publishing repository), use two separate remotes.