Frog kicks have a load, a power stroke, and a glide ... they're good for covering long distances at moderate or slower speeds.
Flutter kicks have alternating load and power strokes ... while one foot's loading, the other is providing power ... and they're best used for diving into current or for covering shorter distances at faster speeds.
Both kicks can be moderated for circumstances ... relying on more ankle than leg motion. These are generally useful for precision movements in areas where you're not going to be moving around much, and possibly in areas where a stray thought can silt the place up.
Different fin types will be optimized for certain types of fin kicks ... for example, you get the most efficiency out of a flutter kick in splits, and the most efficiency out of a frog kick with stiffer blade fins. This doesn't mean you can't do alternate kicks in fins that aren't optimized for them ... but rather if there's a type of kick you prefer to use most often, the choice of fin should be made accordingly.
People claim that a flutter kick tends to silt ... but my experience is that if you flutter kick properly it's no more likely to silt than a frog kick. As you're swimming, it's important to keep your fin tips in the slipstream. Split fins are easy to kick, and people tend to overkick them ... getting them out of the slipstream, which creates a swirl of water below you that results in silting. The main reason for this is that a lot of divers seem to be in a hurry to get somewhere. Meh ... when I'm underwater, I want to slow down and see what's around me ... so whether I'm frog kicking or flutter kicking, I'm generally using the "modified" style that's more like flicking the fin tips than putting any real effort into it.
As I explained to some fellow divers once ... I'm like a draft horse, I can go all day, but I don't like to "run" ...
... Bob (Grateful Diver)