This has been covered here in this forum quite a few times already, but here's a brief overview...

Patented plants cannot be legally, vegetatively reproduced (this, of course, would include cuttings) for ANY REASON (including for your own personal use) without the consent of the patent holder. You could trade a purchased, patented plant with someone as long as you gave them ALL of the plant in your possession (not just a cutting, while you keep the original plant).

Patented plants may be legally sexually bred to produce seeds. In certain cases (mainly with certain types of crops), other legal limitations may apply to seeds (these would include variety protection and genetic/plant utility patents).

Trade marks have nothing to do with what you can grow, only with what you can call what you are trying to sell/distribute. You are perfectly free to reproduce non-patented, trademarked plants and sell/distribute them using their real cultivar name. You just can't use the trademark name without permission. Plants can be both patented and trademarked, or just have one or the other.

Patented plants are supposed to be well marked as patented when sold. So looking at the tag is one way to tell if the plant is patented. You can also google the name along with the word 'patent'; which would normally turn up a patent with ease. One super option is the plant patent section of Patent Genius. All plant patents are listed, but you may have to look a couple of different ways to confirm that something is not included (some are categorized in weird ways).