What determines the top speed in ice skating?

In ice hockey skating, you want maximum maneuverability while in speed skating you want the fastest speed. To maneuver on skates requires a coefficient of friction higher than that of skating straight ahead. I don't know what the skates look like but I'd think the sides of the blades would have high coefficient while the bottoms would have lower.

Two important things come into play:

1) Air resistance and friction with the ice. Kinetic friction is not completely linear, but it won't increase with speed the way air resistance does. Air resistance will be a significant force at 25 mph.

2) Leg Speed. To exert a propulsive force on the ice, when you go to accelerate you must be moving your foot at more than 25 mph since that is how fast the ice is moving relative to your body to begin with. This is, incidentally, also the major limiting factor for runners, and the reason why people can get to much higher speeds on bikes.

As Nuclear Wang points out in the comments, bikes don't completely skirt this limitation - they are limited by tire speed which is limited by leg speed. But the mechanical advantage of the pedal system allows the tire speed >> leg speed

The two big factors are air resistance and skate edge.

Air resistance increases as the square of speed. At 25mph, for example, about 90% of a cyclist's effort goes into overcoming air resistance. Speed-skater's slippery clothing makes a big difference at high speeds.

A skater propels themselves forward by pushing side-to-side, not forwards-backwards, with their skates at an angle to the direction of travel. At higher speeds, your skates need to make a smaller angle relative to your forward motion, and this means you need a longer, straighter edge on the skates to be able to grip. It's a bit like a lever (small movement one end can make big movement the other), or perhaps a sailing ship (angle the sails right and you can go faster than the wind is blowing).

Hockey skates are curved for manoeuvrability and you'll run out of edge pretty quickly. Speed skates have very long, sharp straight edges, so they can grip and produce useful forward force even at very high speeds.

As with most limiting factors with regards to speed they are usable input power, and power dissipation.

Input Power

Human legs can provide power by pushing with a certain speed, higher force and higher speed increase the amount of power available. Human muscles cannot apply the same force at all speeds but rather as the speed increases the force that the muscles can apply decreases. This decrease isn't exactly an inverse relationship, so the amount of power available depends on the speed of the action with a maximum somewhere in the middle.

Maximizing Power

Anyone familiar with bike gears understands that by changing your gears you can change how effective you are at pushing the bike forwards. What a rider is doing by changing gears is changing the speed at which their feet must move in order to produce thrust. This can be used to tune that speed to match the speed at which the rider produces maximum power.

A similar mechanism can be used in the case of ice skating: the angle of the skates. The angle of the skate determines the ratio between the skaters forward velocity and the skater's foot's velocity. Just like with the bike, this can be used to tune the speed to match maximum power output.

This is very different from running for example, where the runner has no choice but to move their legs at the speed they are running.

Power dissipation

In all of these cases you can keep accelerating until your power output is exceeded by your power dissipation. In the case of ice skating there's air drag and skate drag.

The skate drag for ice hockey skates is higher than for speed skates due to their shorter/more curved blades¹. This results in a higher effective coefficient of friction. Interestingly, this coefficient of friction comes into play with determining the ideal angle of skates. If the skater chooses a shallower angle so they can move their legs slower and apply more force, then some of that additional force is eaten up as additional power dissipation from the increased friction. So it turns out that the skater should actually choose a slightly wider angle than what would allow them maximum power output as that slight bit of additional power would be eaten away by additional frictional losses.

^{1: "An 8’ radius is flatter and provides more speed as there is more blade touching the ice" From the radius section}