What does this mean when it comes to moving individual supports on a handrail? Well, the rules are equally weird, but differently weird.
In the following example, you might want the spacing to be measured horizontally (in plan), so you need to move the supports on the sloping parts of the handrail.
The first thing to do is select just the support (Tab, select), and unpin it. This will allow you to slide the support along handrail - but most likely you want to be very precise about how far it is moved. You might try using the 'Align' tool, providing you have something like a reference plane to align to:
Law of Diminishing Returns
In this context, the Align tool does not do what you expect - it presents you with more Revit Weirdness. Once you select the reference plane to align to, then click on the support centreline, it moves the support only about two-thirds of the way (this fraction probably varies depending on the slope of the railing).
If you try Align again, it goes another two-thirds of the remaining distance.
Try again and you get closer - but you will never quite get there. There has to be a better way?