'traditional' cheap stick welders output AC and have the simplest controls possible; for example
this is typical. The big knob in the middle adjusts the current output by a simple transformer; the adjustment is actually performed by sliding an extra piece of soft iron in and out of the transformer core, which affects the total flux linkage between secondary and primary windings, and therefore the output of the transformer.
IME such welding sets work quite well (for hobby uses) if you use them in the upper part of their current range. However IME if you take a 150A set of this type and try to use 'sparklers' (1.6mm rods, which require 20-50A) on thin section material then you can have the most miserable time you can possibly imagine; bird poo, unstable arcs, blow-through, rods sticking, rods wobbling around, you name it. In fact I would go as far as to say it is often 'impossible' to stick weld using this combination, if you are an inexperienced welder.
However is not 'impossible in absolute terms; I have seen skilled welders make really good welds in situations that I have found 'impossible'. The welds look fine, the welding process looked stable etc whilst they were welding but afterwards they will often say 'that was a bit tricky' or 'I wouldn't want to do that all day' or something like that. So I have seen skilled chaps use the thinnest electrodes and they welded car bodywork thickness steels using some crummy hobby welder and they made it look quite straightforward. I have done quite a lot of welding (various ways) and I find the same thing nearly impossible.
Modern stick welding sets are increasingly becoming switch-mode type and these sets output DC. Crucially they behave much better at low currents and are usually easier to weld with at any current. They were quite expensive, but you can now buy a nice switch-mode type welding set for cheap; eg there is one that is sold by Aldi and it costs just £60.
https://www.aldi.co.uk/workzone-inverter-welder/p/085506226214500OK it only goes to 80A but this is enough for 2.5mm electrodes. [I have a 'proper' set and it is a similar size but does 200A off a 13A plug; however it did cost a lot more...]
You can often use the same PSU for scratch-start TIG too. I suppose that if a cheap MIG welder blows up you would be able to rebuild it using such a PSU.
Soon the only reason for buying a 'traditional' (AC transformer) stick welding power supply is that for some reason you want to use AC, and/or you expect to leave the thing for extended periods in a damp shed and want it to work when you come back to it. I leave my inverter welding PSUs indoors where the damp won't wreck them.
cheers