Many saddlebags use basic velcro straps attached to your saddle rails. This is the lightest weight and arguably the most secure option. But, if you're using a dropper post, a bag that utilizes a velcro strap around the seatpost to stabilize the bag may prevent your saddle from lowering all the way.
Of course, every brand in the bike industry is continually searching for a point of difference, and thus options that use a bracket on the seatpost or saddle rails also exist. These are often a bit heavier and we have seen a few hit the eject button over drops and through rock gardens, but they make swaps between bikes painless.
Regardless of how they attach to your bike, most bags will utilize a zipper to keep everything inside, while others will be more of a roll type which may use buckles or even Boa dials.
When it comes to carrying spares, there is no reason to restrict yourself just to strapping a tube, multi-tool and a couple of CO2 canisters under your saddle; there is a heap of great options that utilize the front triangle of your bike for storage.