Of course there is a difference, else there wouldn't be two different methods with different names.

If the load is floating, like a motor or solenoid for example, then high or low side switching makes no difference to the load. That is because, by definition of floating, the node only "sees" the differential voltage accross it and doesn't react to the common mode voltage.

Even with a floating load, the differences to the driving circuit for high versus low side switching can be significant. By convention, we usually consider ground the negative side of the power supply driving the control circuitry, with power then being positive. Since ground is the negative side, and other signals we may need to interact with that connect to the rest of the world will be referenced to this ground, the control circuitry is then also ground-referenced. For example, even if you're driving a 24 V solenoid, the microcontroller producing the PWM pulses will be powered by a 3.3 V rail and ground.

Since the control circuitry is sitting on the low side of the power (the ground), driving low side switches is usually easier than driving high side switches. Therefore, with a floating load that doesn't care whether we switch the low or high side, we usually switch the low side.

Another reason for using a low side switch is when one side of the load is already connected to the positive supply beyond our control. The only choice we have is to leave the low side of the load floating to turn off the load, or connect it to ground to turn it on. It can be convenient for some loads to be pre-connected to power on one side to simplify overall system wiring.

In some cases the load does care. If the load has other ground-referenced signals it has to connect to, then you usually need to keep its ground node connected to ground. In that case, you have to switch the positive power to the load whether you like it or not. Again, this is usually more complicated than driving a low side switch, but not overly so that it requires great lengths to avoid.

When switching the low side with low side control circuitry, it's pretty obvious you want to use a NPN transistor or N channel FET. However, with a high side switch you have to consider more options. N channel FETs generally have better characteristics as switches, but using one presents two problems: The gate has to slew over the switching range plus the gate on/off range, and it needs a voltage above the power rail when on. There are driver chips that can take of these things most of the time, but there are still issues.

A P channel FET is easier to switch as the gate voltage only has to range from the power voltage to around 10 V less for most FETs. PNP transistors can be even easier since you only have to draw some current out of the base to turn them on. However, turning them off quickly can be a challenge.

So, as usual, there is no universal answer, and the tradeoffs have to be considered separately for each application.