The story of critique partners, and alpha and beta readers starts with a couple of questions. Who do you trust? When is it safe to trust, and what problem are you trying to solve?
Critique partners tend to be other writers, people in the trenches doing the same work. In healthy groups, everyone works toward the common goal of making the books, stories, and writing better. A healthy critique group can foster life-long friendships, sure, but they can also make better writers. They're inspiring. If you like the group, you want to write just to have something to take to the meetings. Bad groups drain you. They leave you feeling diminished and exhausted even if everyone was pleasant. They zap your writing energy. If you find yourself in one, get out. A critique group needs to be a circle of people you can trust with tender, newly born ideas.
Critique groups, when they work, solve the biggest writer problems. They can help take a raw, nascent idea and brainstorm with you to flesh out the world, conflict, plot, and characters. A healthy group will not only identify your weak points as a writer, they'll actively help you strengthen them - while you help someone else strengthen theirs.
These are the individuals you can trust with a crappy first draft. They're usually either authors themselves or very knowledgeable readers who can speak to things like motivation and goal mismatches. Or characters not following through on a piece of foreshadowing you dropped in chapter two. These brave readers search out plot holes and point out spots where the story map loses the reader. Usually, alpha readers already know the story. If only because most of us rely on our critique groups to be alpha readers. I can trust these readers to take a novel that's 2/3 written and tell me where I went wrong. Or right.
Beta readers read for sense, flow, and enjoyment. By the time a writer's idea gets to these readers, most of the issues have been ironed out. The story is generally complete and approaching polish. It might still be rough around the edges, but this group of readers - and they usually are readers rather than fellow authors - are the fine grit phase of running your story through the rock tumbler. You'll get grammar notes and maybe a few 'didn't understand this' beside some paragraphs or scenes. But by this point, no one should be pointing out plot holes you can drive trains through.
As for when to trust - that's trial and error. When I first started writing, I needed a critique group while I was drafting. Now, I want a complete rough draft before I expose the work to other eyes. Receiving feedback while I'm drafting has become too disruptive. Finding all that out was pure process of trial and error. So was finding a critique group that didn't suck the joy out of writing in the first place. It took a few tries.
Moral of the story: Writer know thyself. And if you don't, experiment until you do. Feedback fuels some writers and crushes others. Neither one is wrong.