No, a commit is not the SHA-1 of the diff. The fundamental object model of Git does not store diffs, it stores the actual state of the source tree as represented by a commit. For instance, here's a commit file [1]—
$ git cat-file -p fdf4fc3
tree d8329fc1cc938780ffdd9f94e0d364e0ea74f579
author Scott Chacon <schacon@gmail.com> 1243040974 -0700
committer Scott Chacon <schacon@gmail.com> 1243040974 -0700
first commit
A commit object just points to the tree object (in turn, another SHA-1, this time of the complete directory listing) and other meta information such as author name etc.
[1] https://git-scm.com/book/en/v2/Git-Internals-Git-Objects