git remote add just creates an entry in your git config that specifies a name for a particular URL. You must have an existing git repo to use this.
git clone creates a new git repository by copying an existing one located at the URI you specify.
Try this out:
# git clone REMOTEURL foo
# mkdir foo
# cd foo
# git init
# git remote add origin REMOTEURL
# git pull origin master
Now there are minor differences, but fundamentally you probably won't notice them. As an exercise left to the reader, compare the .git/config's from each directory.