Here's the difference...

As a whole cash vs tournaments the idea is to make money... Playing cash I.E you buy in for $300 (10% rule) you should have $3000. In your bankroll then to account for badbeats and swings etc. you might only be able to play 1 day per week or 2 if you are working a job full time. The idea is to make a certain amount per session, lets say you buy in for $300. Your goal may be to make $150. (50%) or maybe you buy in for $200 your goal might be to make 100% or $200. Per session. After you make your goal weather it be in 30mins or 4 hours you stop for the day and log it. This will help teach you bankroll management and how to treat poker like a business and that its a marathon over a lifetime of sessions. Also in cashgames you can wait for good hands or flopping the nuts and win a big pot or post flop make overbets because you don't want people catching cards n sucking out, it's better to win a little than lose alot. Half the $1/2 players are either playing with a small bankroll or (lost money) meaning they go in expecting they will lose it n it's ok...

In tournaments the goal is to sometimes allow people to chase for their cards so you get value for your hand, since the chips don't technically cost anything (except your initial buy in) it won't hurt you as much psychologically if someone sucks out in a tournament on you as it will in a cashgame. Also once you get into bigger tournaments lets say a $150/$250 buy in with a $100,000 prizepool Guarentee you will only cash/win 10% of the time or 1 in 10 tourneys. There are set dates+times for these events and in different states once you travel the circuit to play these. ($200/ $100,000, $350/ $300,000, $550/ $1Million guar. prizepools) big tournaments have players that not only just play because they love the game, some dedicate our entire lives to poker 6/7 days a week and take it really serious. Cash game players tend to be more recreational players meaning you can go 24hrs at anytime of the day or week.

The difference between $1/2Nl and moving up to $2/5 or $5/10 cashgames is clearly bankroll and skillset also trying to get more $ per hour based on play or ROI. Guys that play $1/2 are technically "learning" the game make TONS of mistakes like playing more hands because its cheaper to see a flop usually ($5-$12 if someone raises) the goal is to always have only 2 players maybe 3 tops going jnto the flop so you have a better chance of winning and where as $2/5 a standard raise preflop is $40. $5/10 it's $75 to $150 so that narrows your opening range down by alot, meaning you won't be paying sh*tty cards like most do in a $1/2 game.

Hope this helped in anyway.