DSLR's are medium-high end cameras, they're pricey (cheapest are somewhere around £5-600) and they're sorta bulky, but only to accommodate all the lenses and shit they need to take really good pictures, with MegaPixels (MP)'s well beyond everything else with picture-taking abilities, and most are also able to be used as a video camera. These are not really suited for amateurs or as starter cameras as they cost a bomb, and although they have an automatic setting, you won't get the most out of the camera's power to make real use out of it without knowing a bit about ISO's, light intensities, apertures, lenses, and shutter speeds, as well as what a RAW file is.
Compacts are what it says on the tin; small enough to fit in your pocket, at the cost of higher quality (similar MP-resolutions as a high-end phone), but are significantly cheaper, which can be under £100 if you get an old model. Great and cheap for starters, but may be limited in features such as only producing JPEG images that are harder to edit later on, might not have filming capabilities, and may or may not be limited to an auto-only setting (so you can't do specific focus on a subject, change the aperture, etc). Compacts can also have niche features, like being waterproof (good for diving or underwater photos), or being generally more rugged than a DSLR.
Compact DSLR's are a more recent thing - more compact than a DSLR, more features and quality than a compact, and somewhat in between the two for cost (between £3-400, but getting ever-cheaper). They may not have DSLR super MP quality, but are far less bulky, have filming capabilities, can have the niche features of compacts, and have slightly cheaper options available.
There's also the older SLR's (the D being Digital in the above) and 35mm film cameras. These can be dirt cheap because of their age unless it's some "classic/vintage model", but are a lot more finnicky because the tech is likely to have come from the 90's or earlier (i.e. no pre-/post-shot preview screens, limited indicators on shutter speed/aperture/light intensity, film is far more fragile to heat/light/cold/humidity/water/dust, x-rays and other radiation, etc), plus it's a constant cost to replenish the film, which depending on the camera and film type, can be very rare and/or expensive. The upside is you get a "classic" camera, with the mechanical bits and clicks, actual film, getting back negatives and actual photos, that sorta thing. It's kinda popular with hipster types, old folks and hobbyists.
I myself have a compact DSLR (Panasonic Lumix something or other) and an old Minolta 35mm from the 80's. I've been using the Lumix for ages now to learn how to do all the settings manually with the help of the preview screen to see the results before I click, so that I can transfer over and use the totally featureless 35mm and gauge what settings I need at the time to get a decent photo out of it.
Anyone here know about high quality cameras?