most of the strips and trays work with hydrogen peroxide.
You have some way to keep the "medicine" against your teeth for half an hour or longer, and it effectively cleans/bleaches it. (It's not recommended if you have sensitive teeth to begin with)
I've used the dissolving Crest White Strips and Aquafresh White Trays. I like the trays better because I don't like how the Crest Strips are also laying against the inside of my lips, and since I don't like the taste of it, I end up just keeping all the dissolved spit and gunk in my mouth until I spit it out half an hour later.
The trays aren't meant to be swallowed, and mostly stay in the trays (I remember taking a napkin and wiping the gunk off my teeth afterwords), but my lips didn't feel like they were exposed to the acid as much, and it felt easier to apply since I kind of put my teeth in them, then pushed the gunk in the trays against my teeth to make it stick. (The crest strips as soon as they touch anything in the mouth, they begin to melt)
Those are the only two I've really tried.
I know a lot of people like the white strips and didn't like the trays though (since you're not supposed to swallow the tray gunk you still end up sitting there if any of it slides out of the trays...but I'm doing that either way) the tray gunk was more of a snot texture though, instead of a melted bubbly ick foam thing. I can't imagine the strips are necessarily good to swallow either though, probably just safe enough to not make you sick from one set of strips.