The way you tell is you have to go very slow. If the bit cuts into metal you wilk know. Hard to cut sheet metal though. Use a wood backer, and do not holt the sheet with your hand. Make sure that when the bit grabs the metal and it spins (it will spin) that all body parts are clear of its path. I just clamp shert metal to wood. I still stay out of the way.
We use those hole saws on metal all the time. When we need to add a line to an existing pipe we drill a saddle fitting. All our trucks go through a lot of these. There is a kind that has carbide teeth spaced pretty far apart. They look like they're not for metal, but they are. They cost 40 or 50 bucks, but they cut great and last forever.
The arbors are sold seperate from the hole saws, and you can get new 1/4" pilot bits also. Don't use a regular drill bit, the pilot bits have a notch or a flat ground into their side for a set screw. The arbors come in 2 main sizes, and a couple of other weird small sizes.
I think the thin type oldgoaly mentioned are a thin nested set, (guess.) You can sometimes tell by the teeth, if it looks thin and closely spaced I probably wouldn't use it on metal. In fact I would use the regular hole saws like you have there. Another thin hole saw has a hole with two flat and two round sides. These are cheap hole saws. They will cut metal, but not much. Im not too impressed eith their wood cutting either.
The packaged bits are for dremel type tools. You can use them on anything, but don't go too fast. Add water if cutting stone or glass. Those that have 1/4" shafts are more for die grinders. I wouldn't use them on a hand power drill. My dremel motor has a foot pedal that controls speed. Start out slower than you think you need to ho, you can speed up when you are more proficient.
I think Rusty got some crappy ones, there are a lot of those out there - even the diamond sintered ones sometimes.
Those rasps are great. You can use them on plastic and drywall too. Stone carvers use them on softer material. They are not for air tools, more for vsriable speed drills. Again, no need to go quick at first. Ive used them on aluminum snd clear plastic. If you go fast at all on plastic it melts and gums up the bit. Go really slow on plastic. Wear eye protection with all these bits, they fling little sharp bits worse than a grinder sometimes.
Chilly
