When you hear someone say that, they are usually using a DSLR which is a automatic camera that will take photos as long as your finger is on the button. While for something like a point-and-shoot camera (which is much cheaper), you can only take one photo picture per click.
To answer the pictures question, I’ve been in possession of several cameras from a wide spectrum of their purposes. My favorite is a DSLR and the one I use right now is a Canon EOS Rebel T7. I like cameras like these because you have a lot of control on what you want to do because you manually adjust everything like zoom, focus, shutter, etc. And that’s how I come up with photos like these. It is true that you don’t get “great” photos often, I would say only 1 out of every 30 bird observations I submit on iNat would be considered 5/5 quality, but most settled between 3-4 out of 5 like this. The big downside to buying a DSLR is that they are expensive, I got mine for $500 and the Nikon D3000 I had beforehand was $400. You might be able to get a bargain price of a used camera on Amazon but besides that, they seem to be out of your budget.
My recommendation with the budget you set is to get a simple point-and-shoot camera and the big thing you need to decide is, how do you plan on carrying it. The Canon Powershot ELPH series is a fantastic little camera because they can easily get 4-star photos and they fit in your pocket. You can get one of those for $100. The Canon Powershot SX series is a larger camera but has more technically aspects. They can range from $200-400 depending on which one you get. The big downside to these cameras though is that they run through batteries like there’s no tomorrow. My last piece of advice is, wherever you get your camera, get it from Walmart because every other company could charge up to $100 more for the exact same camera.
In terms of filming tips, my best advice would be closer zoom does not equal better photos. You will want to zoom in on your subject but you shouldn’t be zooming all the way in or have subject fill the frame. Taking a wide shot and cropping tends to produce much better photos than excessive zooming. Two, light is your friend, so use it to your advantage. Unless you can’t, always position yourself between the subject and the sun. Hopefully this helps.