Does an MDM solution require special apple devices

does the usage of an MDM solution (like Apple Business Manager/Apple School Manager) require special Apple devices that are only intended for this kind of purpose?

No. There is no such restriction in place.

You can enroll your personally owned devices in a MDM solution of your choice.

You are possibly confusing it with Apple's Device Enrollment Program where businesses can procure devices from Apple or approved resellers, get them shipped to the users and have them automatically enrolled in their MDM solution.

But even such devices are same as the regular devices. Only different being that during device activation process, the device communicates with Apple servers and see if it's unique serial number is already enrolled in a MDM solution and configures itself accordingly.

Short answer: No.

There are no special Apple devices for device management. All Apple devices (Macs, iOS devices, Apple TVs), even used ones, can be setup/prepared for device management.

The following Apple support doc might be a good starting point: https://support.apple.com/en-us/HT207516

Most device management solutions like Jamf have extensive documentation and support areas, so depending on the vendor/solution you have in mind, it would be a good idea to check out their documentation.