If you go to the list of branches for a repository, you can click on ... (More Actions) on one of the branches and choose Compare branches
This will take you to a URL in the form:
https://dev.azure.com/{organisation}/{project}/_git/{repository}/branches?baseVersion=GB{baseBranch}&targetVersion=GB{targetBranch}&_a=files
You can then change the baseVersion and targetVersion parameters in the query string. These can take the following forms, and can be mixed and matched:
GB{branchName}GC{commitHash}GT{tagName}
Just in case that link gets broken, clicking “View Merge Changes” on a pull request takes you to the same page but with a slightly different URL https://dev.azure.com/{organisation}/{project}/_git/{repository}/branchCompare?baseVersion=GC{baseCommit}&targetVersion=GC{targetCommit}&_a=files
I’m not sure if there’s a nicer way of comparing commits from the UI, as it only shows branches and tags, but if you do it this way you don’t have to temporarily tag commits or create temporary branches just to get a diff that shows all of the changed files.