Let me explain in simple terms. When it comes to rewards, POS is like POW but you just need to hold your coins in a wallet that can stake. In general, the rewards doesn't necessarily comes from transaction fees alone, rewards can also include new coins that is mined from staking and is added to the circulating supply. Though reward distribution method varies from different projects.
so aside from transaction fees and rewards from newly mined blocks, are there any other methods to generate these earnings? and do you happen to know what are the methods used in the projects i mentioned in my original post please?