For bears:

If it's black, fight back. If it's brown, lay down.

Black bears are just like big dogs imo. You are supposed to get as big as possible, and scream profanities at them. That usually scares them away. A griz (brown) is not so easily scared away. Your best bet is to lay down and cover your vital bits and hope it gets bored before it mauls you to death.

Black or brown (black bears can be black, brown, or blonde, but a griz is always brown), you should always carry bear spray if you are in bear country, and only spray it if it charges you. Unless you carry a shotgun with deer slugs in it, you won't even hurt an angry grizzly, let alone stop it.

If you piss one off, black or griz, that happens to have cubs with it, all bets are off. Use your spray and hope for the best. Just never run from one because then their predatory instincts kick in and they chase you.

You likely won't even see a mountain lion until it attacks; they stalk their prey. So if you do see one, it has likely been following you for a while. Grab a knife or something and be ready to fight. Protect your neck and throat as those are the targets for when it tries to kill its food. They rarely attack full grown humans, but are known to go after dogs and small kids much more often.