Agronomically hops are a bine, a sort of vine variation that climbs by spiraling around some sort of support. They are invasive, shooting 20 feet into the air (if given proper support) while the rhizomous roots propagate along underground, ready to send more climbing tendrils out the following year.
Both have a mild continental spiciness. The differences are likely to be subtle, and I expect that I can substitute one for the other and produce a reasonably similar beer. Hallertau is a quintessential delicate German flavor, but American brewers have pushed Crystal into some unexpected realms, none more adventuresome than Rogue’s excellent (though no longer in production) all-Crystal Brutal Bitter and I’ve used it in everything from wheat based blonde ales to porters. Go figure.