Matrix is the protocol, Element is a client to access Matrix which it does so via a matrix homeserver (which then federates across the rest of the Matrix).

So Element is free to use, but there are a range of servers to choose from. The matrix.org server is free to use, though as the largest single instance on the public federation is run on a best effort basis.

Alternatives are to either host your own server, or have someone else do that for you. The payment plans that you are looking at reference Element Matrix Services (EMS) which is a SaaS offering allowing you to spin up your own server to be used by whoever you choose to give access to (friends/colleagues etc). The advantages being that you get grater control of your data and improved performance.

Using email as an analogy

Matrix = Email matrix.org / Matrix Hosted Services/ some other server = Fastmail/Gmail/Hotmail etc Element = Thunderbird