No, the software itself is open source and licensed under the AGPLv3. There is no difference in functionality between an installation with a subscription and without.
The two things you can get with a subscription is access to our enterprise repository, which contains more thoroughly tested packages, improving the stability of your system, and our enterprise support. If you want to know more about what is included in a subscription, you can read our Subscription Agreement [0], with about 5 pages it's not that long of a read.
[0]
https://www.proxmox.com/images/down...-Mail-Gateway-Subscription-Agreement-V2.2.pdf