Bonsai are just trees and shrubs, so no, there is no bonsai specific rooting hormone. Similarly, there are no such things as bonsai seeds or bonsai fertilizers. Although there are fertilizers marketed to bonsai enthusiasts, they would work on other plants just as well as bonsai.
There are different strengths of rooting hormone available, as some species root better with higher concentrations. I have only seen the common (I believe .1%) in local stores though. Rooting hormone is no magical elixir or guarantee of success, consider it an aid. Good cultural practices are still the most important element when rooting cuttings.
Do not use the rooting hormone for seeds that is not what it is intended for, a seed already has an embryonic root contained inside so the hormone is unnecessary and perhaps even detrimental.
I'm not sure of the recommendation of 'for outdoor use only' I have used (the powdered version) inside. If your not afraid to use it outdoors I see no reason that you should not, with common sense, use it indoors. I'm sure it is used in greenhouse situations.