tl dr: If you don't tax your vehicle, this should not be an issue.
I'll answer the second part of the question first ...
What's a speed rating, anyway?
Here is what National Tire and Battery (NTB) has to say about speed ratings:
The speed rating tells you the speed the tire can safely maintain over time. A higher speed rating usually means you will have better control and handling at higher speeds — and that the tire can take the extra heat. As a general rule, tires with higher speed ratings also handle better at slower speeds.
The U.S. Department of Transportation (DOT) set the ratings scale, shown below. But tire makers test their own tires and assign their own speed ratings. On the sidewall of every tire, you'll find one of these speed rating codes:
M — Up to 81 mph
N — Up to 87 mph
P — Up to 93 mph
Q — Up to 99 mph
R — Up to 106 mph
S — Up to 112 mph
T — Up to 118 mph
H — Up to 130 mph
V — Up to 149 mph
W — Up to 168 mph
Y — Up to 186 mph
Z — (See Below)
What does 'Up to 99 mph' really mean?
Tires with a Q speed rating can safely sustain speeds of up to 99 miles per hour. The tire may be able to reach higher speeds, but going faster than 99 mph for any length of time is not safe. The tire is not designed to handle the stresses.
What is a Z Rating?
For tires rated above 149 mph, a Z rating may appear in the size designation.
Safety and Speed Ratings
When you get new tires, choose tires with at least the speed rating your car or truck's manufacturer recommends. It's ok to move up to a higher speed-rated tire, but don't go lower.
The speeds shown are test speeds; they are not recommended speeds. Please obey speed limits. We want you to be safe.
As to the first part of your question:
... does it really matter if it differs between axels, as long as all else matches?
It depends on how you drive your vehicle. If the vehicle is used only as transportation, it probably would never make a difference. As stated in the article, having a different speed rating will affect how the tire handles overall. If the tire is never taxed to its limits, you'll probably never see it.
As Criggie stated, every vehicle is going to have a minimum recommended speed rating which will be associated with the vehicle. If you never exceed posted highway speeds, you'll probably never have to worry about this as you'll never get close to it. If you keep the same rating on each axle, you shouldn't have any issues.
There are some aspects which you need to consider. If the "old" tire are designed as "run flats" and the new ones are not. Run-flat tires are usually fairly high performance tires. They have very stiff side walls and can stand up to a lot of abuse. Having these on one end of the vehicle and normal tires on the back will most likely cause you driving issues as the difference between the two in drivability would most likely be seen. I mention this because the run-flat tires will most likely have a higher speed rating than normal tires and may be the situation you're looking at. In this case, I'd highly suggest getting all four tires changed.