Is it okay to apply for two different positions at the same company?

I personally don’t see anything wrong with applying to 2 different positions within the same company. As long as you’re upfront and honest, it shouldn’t ever be a problem. Find out who is in charge of hiring for each position, and if it’s the same person or department, just let them know you’re interested in 2 different positions. If there are 2 different hiring managers or departments, just apply to both normally.

Two is quite reasonable, especially in bigger organizations. Forgive me for stating the obvious, but be sure you are actually qualified for both jobs, and write different cover letters for both emphasizing your skills as they apply to each position. Be prepared to say what interests you about each position in a sort of compare-and-contrast way.

It doesn’t sound like you’re doing this at all, but I’ve seen people turn in separate applications for every job in a given department, usually without regard to their qualifications. Candidates that basically spam with applications can leave a bad taste in resume screeners’ mouths. They also look desperate.

Best of luck in your search!

Just be sure to have a well thought-out and convincing answer for “Why do you want this job”. And you can’t say the same in both interviews – if you’re going for 2 positions, chances are there’s an overlap in the interview panel, it’s the same HR person involved, or the recruiters just compare notes, so any inconsistencies (like saying this one is your first choice) will be discovered.
Saying you want to work for the company might work if you’re going for an entry level position, but beyond that, they’ll want to know that this is exactly the challenge you’re looking for, what you want to do and you will bring something amazing to it.