Actually, it's semantics, but active generally refers to visible lesions. You can shed virus without having an active lesion (asymptomatic shedding), but the risk of transmission in that situation is very low.
Although the oral herpes virus (type 1) and the genital herpes virus (type 2) can both cause the opposite kind of disease (oral or genital), the chances are lower for the opposite. Plus, if you get type 1 causing genital disease, the risk of recurrent sores is much lower.
My wife got type 1 many years ago, and I've been spared all these years because she's careful about what she does (!) when she has an active lesion.
Plus, about half the population already has antibodies to type 1.