I just looked into uniglide casettes since I recently got my first cassette bike. And I noticed that cassettes used to come in two flavors, at least, uniglide and hyperglide. I know uniglide is not used anymore nor for years but about when would we find them and on what brands and models?

It's more about what hub is on the bike. CAme out in 1978 so any particular bike could have had wheels changed in that time.

​​​​​​https://www.goatsurfer.com/assets/Shimano_1978.pdf

I've picked up NOS Uniglide hubs in the past primarily for the hubs they were part of... Since the Uniglide cassettes were tough to find (and expensive) I would replace the freehub body with a Hyperglide. Made life easier.

Sheldon Brown has you covered. Uniglide has twisted cog teeth, whereas Hyperglide were shaped specifically for better shifting etc. Uniglide with no specific "wide-narrow" alignment spline. Hyperglide with one.

Also, there are two flavors of Uniglide. The original, a press-on mount of the freehub to the hub body, are not replaceable. The 2nd gen model bolted onto the hub body. These can be readily replaced with Hyperglide freehubs. I've seen both, with the 2nd Gen freehubs on a 1988 Trek and 1989 Fuji, if these dates help.

Just to add on to this -- when you have a model number, you can still find Shimano technical documents through their own website. You can use their exploded diagrams to validate whether a Uniglide hub you're considering uses a fixing bolt to hold the freehub body or just uses the locknut assembly to hold together. If it uses the fixing bolt, the body can be replaced with a Hyperglide body. There may be fit issues with the seal between a specific freehub body and a specific hub shell -- I'm not knowledgeable enough about those fitment issues to be helpful, but it has been covered in other threads, so there is information available.