The linear velocity of the outer grooves of an LP is roughly 25% faster than that of the outer grooves of a 45. As they both track towards the centre the 45 ends up about 35% faster than the LP.
The choice of speeds is messy, as it relates to both frequency response and also the level the recording is cut at. As the groove wiggles, a loud component requires a bigger wiggle, but the geometry of the system places an upper limit on the angle of the wiggle - too steep an angle and you will end up with problems that will result in distortion or mistracking. So, within a defined frequency range and dynamic range, there is a trade-off between the level you can cut the disk at, and the speed of the groove. Also, a higher cutting level means you need to space the grooves further apart. (There is the complication of the RIAA response, which boosts high frequencies and drops bass frequencies when the disk is cut, and does the reverse when played - in order to preserve the higher frequencies which would otherwise be lost in the noise, and stop the bass frequencies causing a groove that was insanely wide. But this standard is the same for all 45s and LPs, so it doesn’t make any different when comparing them.)
For your standard radio play single, a 45 works well. You get a reasonable groove speed, and you typically don’t have a lot of music to put on the disk, so you can exploit that groove velocity and cut the recording at a higher than standard level. This gets you a recording that is slightly louder, but also has better signal to noise, and lower distortion. That allows the mix to exploit wider dynamics. (There is some irony here, the radio stations will run your carefully crafted high dynamic recording straight into a compressor, and to some extent undo a lot of what has been achieved. There was a certain level of arms race here, with the creation of special mixes designed to sound good when played by a radio station, and special releases of these disk only to the radio stations. They were not actually designed to sound right on a domestic system.)
Once you start to pack longer recordings onto the disk you need to back off the recording level to narrow the effective space taken up by the grooves. If you have a much longer recording you can back off the level to lower than standard, and pay the price with a slightly softer level, and slightly worse signal to noise.
The top end of the dynamic capability is of course the 45rpm 12inch. With only a couple of tracks (I remember when you got the standard track plus the “radio mix” or “dance mix”). The really high groove speed at the outer edge of a 45rpm 12" allowed a very aggressive recording level, which allowed serious dynamic range.