Cash Game and tournaments are different poker variations. The participants play for and make wagers in cash. The participants buy into a table and can bring in new money to the table at any time, so long as they do not step over the maximum buy-in for the table. There exist different buy ins fort he cash game tables. You can join a very small table where the blinds are only 1 Cent/ 2 Cent or you can join also tables with 25$/50$. Cash Game ist he variant of poker where you find always at all online poker rooms the most traffic. Especially at the smaller buy ins you find 24/7 running tables.
At online poker tournaments you pay a fix buy in and play with a starting stack of chips. You can lose only the buy in you have paid in the beginning. At Cash Game every chip you bet an risk is real money. As we already explained in the beginning, you can bring always new cash to the table. The risky thing at Cash Game is that you can lose in one hand all your winnings. On the other side you can of course also win a lot in one hand.
No-limit and Pot-limit games are often called cash game since the players bet as much as they want, as opposed to fixed limit variants where the bet sizes are constrained to discrete steps. Fixed-limit is not viewed as “real” poker in this sense.
You find in every lobby different shorthanded 6 players cash game tables and also fullring tables for 9 players. Of course it exist also to play heads up against only one player. The best traffic you will find always at the 6 max shorthanded and the heads up tables. 10max tables are not so popular anymore as a few years ago. Anyway you can still find some running tables especially at the lower buy ins.