A jointer will give you a flat edge.
A planer will give you an even thickness.
To square up lumber, you typically will:
1. Run one edge over the jointer. You now have 1 "true" edge, 3 unknowns
2. Place your true edge against the jointer fence and run it over the jointer. You now have 1 true edge, 1 true face and they're square (90 degrees) to each other
3. Send it through the planer. You now have 1 true "edge", 2 faces that are flat, parallel to each other and 90 degrees to the true edge
4. Put the true edge against your table saw fence and rip the other side. You now have 2 true edges and 2 flat, parallel faces 90 degrees to those edges
A planer just makes sure the board is a particular thickness all the way through. If your board is bowed, it will leave you with a bowed board that is just the same thickness all the way throuh. The reason it won't work on warps or twists is because the planer will use rollers to "push down" the wood as it goes through, so it will flatten the board as it makes its cuts, but the board will warp once it comes out from under the rollers.
You CAN make a planer "sled" and shim under the board to prevent this, but it can be cumbersom.
I don't have a jointer, but want one.
The problem with jointers is they get expensive fast and you can only face joint as wide as your jointer, which means even if you drop money on an 8 inch jointer, you can't face joint a 10 inch wide board.
What I try to do is use a hand planer to get the wood as flat as I can and then use the planer to get it even thickness. This has worked well enough for me thus far. Then you can make an edge jointing jig for your table saw and finish getting everything squared up.
That said it's not perfect and I'm still learning how to improve. I often run into issues cause my process isn't getting things as square as I need, but I get better each time and learn new tricks as I continue.