The processes are essentially the same, but single stage paint can behave a bit differently than a modern clear coat.

First, the obvious part is that you can see paint transfer onto an applicator pad when using something even as mild as a cleaner wax - if your car is black, the applicator will turn black, a red car will turn the applicator red, etc. Perfectly normal, and the only reason you don't see this on a modern car is because the trace amount of paint you're removing is clear.

Second, single stage paints tend to be more worker, or softer, or more delicate, or however you want to phrase it, than a modern catalyzed clear coat is. This means you can often use less aggressive products to correct defects. Just keep in mind that if you're dealing with original, old clear coat and you don't know the full history of that car, the paint could be very thin in spots. Even if it looks really good, that thinness can bite you when you least expect it. Be careful around raised body lines, panel edges, etc.

Third, single stage paints love products with a lot of polishing oils in them, especially the darker colors. A light cleaner/polish like M80 Speed Glaze from our Pro Line is incredible on dark single stage, whether you're working by hand or with a D/A. The added depth and gloss provided by this type of product can really make those darker colors look deep and wet. Something like M07 Show Car Glaze if the finish is swirl free works great too. You can finish off with any wax or sealant you like after that.

In the end, it all depends on what you want out of the finish (daily driver, show car, weekend toy, full concours prep, etc), how much time you're willing to devote to the process, and what your skill level is.