Restoring from Time Machine to new Mac mini M4

I would recommend doing the following prior to the migration:

On the old machine please do the following:

1. Upgrade all 32 bit apps to 64 bit apps as 32 bit apps will not migrate. You can use the following link to identify 32 bit apps: https://roaringapps.com/collections/list-of-32-bit-macos-apps
2. Uninstall any apps that you no longer want or need.

After you have completed steps 1 & 2 then backup using Time Machine. Then when the new machine arrives follow the steps in Setup Assistant and Migration Assistant

It's really easy and 100% dead reliable and yes the new machine will look almost identical to the old computer's setup including the Desktop. Follow these steps and you should absolutely ZERO issues.

You can try but there is no guarantee all 64 bit apps will run in High Sierra, remember HS is > 10 years old now! And yes, you may find older 32 bit apps were never upgraded by their developers to have 64 bit versions. In that case you need to search for more up to date replacements.

To answer what difference it makes, it makes the migration a bit more simple in that you won’t have to update apps after the fact.

If you take the old computer's Time Machine backup with you when you purchase the MM at your local Apple Store they will help you migrate however it's something that is extremely simple for you to do. AFAIK they will not update old 32 bit apps to 64 bit or help you replace old 32 bit apps with replacement 64 bit apps.

Make an appointment at the store (unless you can wait around for hours) and bring the old Mac's Time Machine External Hard Disk and they will migrate it. You can do the same thing by simply connecting the Time Machine External Hard Disk to the new MM. Just follow the instructions in the Setup Assistant and Migration Assistant link I provided in my initial post. This is so simple you will laugh at yourself for making a "thing" out of it.