"Why is this section even here? None of these words are prepositions." Thank you—that's exactly what we're saying. Astute, Shmooper. Very astute.
People usually think that "to" is always a preposition. It's not. This little word can also be an infinitive marker. You can usually tell if it's an infinitive marker if it's followed by a verb. If it's followed by a noun phrase, it's a preposition. End of story.
Knowing that, we might as well discuss the difference between "try and" and "try to." Everybody will understand what you mean when you say try and. However, by inserting the preposition and in between try and whatever you're trying to do, you're separating these two actions. So if you're going to "try and dance," you will first try, and then you will dance.
So yeah, it doesn't make "logical" sense. This is what linguists call an idiom, or a colloquialism. And it's totally fine to use "try and" out loud because absolutely everyone will know what you mean. However…your English teachers might not like it in an essay. Womp womp.
Example
I want to try and watch every episode of Friends in one day.
OR
I want to try to watch every episode of Friends in one day.
No matter how you put it, it's just not possible. Two hundred and thirty-six episodes times 23ish minutes each (assuming you're watching on Netflix sans commercials and never getting up to pee)? That's like 90 hours—way more than the 24 we've given ourselves here.
But we digress. The first sentence is basically saying, "I want to try to do something that I'm not going to name, and then I'm going to watch every episode of Friends in one day." That's weirdly and unnecessarily mysterious, don't you think? Just stick with try to.