When transferred storage is different from old Mac

No. You should not be alarmed. There is nothing wrong.

Caches, indexing, and temporary files can easily account for these differences.

What is done is done but for further situations like this >>

If the new computer is going to be the Apple Silicon M1 Equipped Computer - would suggest Only Migrating the User Account and nothing more.

1 - Apple Silicon with either Big Sur macOS 11 or Monterey macOS 12 Only Support everything 64 bit and there is no workaround.

2 - Issues that may exist on the older computer will be migrated to the New Computer. This would badly pollute the new Original and Pristine installation of the new OS.

3 -  Applications, extensions and Software Drivers may or may not even work on the new computer.

4 - IMHO - it would be best to only install new application etc Directly from the Developer or the Apple Apps Store.

5 - Due Diligence on New Applications and make sure they are Monterey / Big Sur compatible and factor in the ARMs CPU of the Apple Silicon Computer