Sort of, up to a point. It really depends on what you're trying to do, but axe grinds are quite a bit more complex. Basically with knives you have hollow, convex, scandi, rhomboid, and a few others which are basically just variations therein. The big difference is that with knives the grind is generally uniform across the entire blade and the only real difference within grind-types across knives is the angle. With axes there are essentially the same type of grinds as knives but they are varied throughout the bit to make chisel, banana, half-banana, mitre, and combination grinds.
Basically, the axe acts as if it has two edges rather than just one, and this is because it not only has to cut but also chip. In a sense this means that an axe is like the scandi knife and spoon knife in one. Just consider what the knife does, thin and hollow knives tend to cut deeply but are very difficult to make a straight cut; thick and convex knives don't cut very well at all but are very durable; scandi grinds tend to cut very well and can ride the wood while also turning quickly because of the short grind pivot, and rhomboid grinds ride the wood the best and make excellent cuts but won't turn quite as quick as a scandi.
Axe grinds act very similar to these knife grinds, you want a balance of depth of cut, riding the wood (this would be your angle variation at each cut), and popping the chip (what people often refer to as the high-centerline). A big difference here is that with a knife you would only change angle slightly for very hard woods, as the knife generally cuts the same across wood-types - the angle is mainly for durability. If your knife cuts pine well it will probably cut hickory just as well. Only if you're chopping, making sharp turns, or gouging will you see much difference; and that will be in the rolled edge.
When using an axe even slight variations in wood make a huge difference. For example, white birch isn't much harder than red spruce, but red spruce may be one of the most difficult woods to chop. The birch will pop out very nicely in chips but the spruce is so stringy and saturated with resin that you really have to work to pop the chip. This means a completely different grind (or at least angle) is ideal for each wood. For spruce, more weight helps, along with a shorter edge, and a steeper roll into the bit.
That would be another key difference. With an axe you are cutting with 80-90% of the edge while a knife very rarely uses more than 20% of its edge at one time. The length, weight, and angles of the axe play a much bigger role.
Also, with the axe there is two movements, both in and out. This is less common with knives. When pulling the axe out of the wood the grind also makes a difference. The finish behind the edge helps the wood enter and exit with ease, sometimes this means creating file marks, and one top filer says that he removes the temper behind the edge of competition axes (no details on what this really means, but if he really is removing the temper perhaps this explains why two-piece axes act better in the wood).
I suppose that's a long way of saying, 'depends on what you want to do with your axe and knife.'
