You got it pretty much figured out, a marketing trend
(nothing wrong with that)
Yes, the hosts do take different approaches to make their services "green" but as a consumer you will not notice anything drastic. For consumers, they tend to like "green" providers just because they're being eco-friendly. Obviously not everyone cares about being eco-friendly, but those that do that happen to need hosting services might find a "green" host to be more interesting.
As a provider, there can be some cost savings if you truly setup a "green" facility. How much? That I can't speak for as I never really looked into it personally but I know there are some pros to having a "green" facility, one being costs.