Can one make money running Bitcoin full node?
Just by running a Bitcoin full node, no. However, you can earn few sats by running a full node along with a Lightning node that has a few channels opened.
The coins you're referring to are proof-of-stake coins, bitcoin is proof of work. See the difference between the two[1].
Just to add that you don't necessarily get paid if you run a node, even in PoS coins. For instance, in Cardano[1] there are the core nodes, the edge nodes and the relay nodes while only the core nodes participate in the consensus mechanism.
[1]
https://files.ifi.uzh.ch/CSG/staff/Rafati/Kursat_IS.pdf (page 8)