Assuming you are talking about stain only (no integral top coat of varnish or similar), there is no reason an interior stain won't work in your garage, nor is there any reason an exterior-grade stain is unacceptable.
As far as I know, exterior-grade stains contain extra UV and weather resistance, with a corresponding increase in price. You have no concerns from that front in a garage, hence indoor stain is fine. Exterior stain is fine as well, just maybe a little overkill.
@Graphus brings up a good point about foot traffic, which should be kept in mind for your stairs. Per this website, deck stains have scuff resistant compounds for extra resistance to foot traffic, which may be beneficial for your staircase.
For sealer/finish, it depends on what in particular you're talking about. For the stairs, you'll probably want some sort of deck sealer similar to Thompson's Water Seal or any of its tinted varieties for some additional color. I wouldn't recommend the use of a finish like a varnish on the stairs due to the expected wear.
For the shelves, you can go with a traditional stain and finish routine. Personally, I'm not a fan of the stain and finish all-in-ones like Minwax Polyshades. I feel like they obscure the grain of the wood too much (granted, these are pine shelves in a garage, so you might not care a lot). So, now you're looking at staining the wood first, letting it dry/cure, then applying a varnish of some sort on top. For ease, I would use an oil-based stain, if you desire to stain the shelves. If you allow the stain to properly dry/cure, you can use either an oil- or water-based polyurethane varnish, as discussed in this Question. I like the water-based polys since there is less time between coats.