If you cloned a branch (for example call it "mybranch") then when you clone the repo you will have a branch called "origin/mybranch". This is effectively the status of the branch on the remote.
Then you checkout the branch locally and you will have a branch called "mybranch" - you do your modifications and then you can do a diff between the two branches:
git diff origin/mybranch mybranch
Or you can simply look at the HEAD as in your example. When you clone the repo you will be at the HEAD. When you commit something you will still be at the HEAD, but the previous commit can be accessed as HEAD~1. So you git diff command can be:
git diff HEAD~1 HEAD
Or just look at the log git log
or for a graphical view git log --oneline --graph --all --decorate
and pick any two commit-hash's/tags/branches to compare.
Update
I may have misunderstood the question. From your comments I think you are trying to just do a diff for files who's contents have changed. You can use the --diff-filter option:
git diff --diff-filter=M HEAD~1 HEAD
Where "M" is for modified. you can use "R" for renamed as well if you need that (and you can combine many options, e.g. git diff --diff-filter=MR HEAD~1 HEAD
for modified and renamed files).