Yes, you should definitely use an SSD over an HDD if possible.
Just keep in mind that what matters is the world save location and game assets. What you want is the world saves and game assets to be on your fastest drive, and the easiest way to do that is to change the game directory in your launcher configuration under installations, click the three dots at the right-most position on an installation, choose edit, and put the directory of choice into the box labeled "GAME DIRECTORY". If the folder is empty, it will download assets again and install them to that directory, as well as download your chosen installation of Minecraft (unless it is modded, in which case you need to reinstall the modded version of Minecraft using the same process that you did before changing the game directory, but installing to the new directory instead).
Unfortunately, I get the feeling that you'll see noticeable improvements after installing to SSD, but they'll be subpar, probably due to other reasons. These kinds of issues will most often be due to improper configuration of the system or the game, though it can also be due to software corruption and corrupted system files, or hardware malfunction as well.
Saying that changing the render distance still causes stutters is helpful, but you didn't mention if "low or high" is referring to the FPS and what the numbers were, whether it was consistent or fluctuating, etc.
Last but not least, the last thing we might try is enabling some JVM arguments, but I want to save that for last. In my experience with the game, when I encountered stuttering, it was usually due to garbage collection and/or chunk generation, so if you're just loading a new world all the time to do your tests, and you turn your head, there is a trivial optimization implemented where the game only generates chunks in the direction that you are looking, so every time you turn your head in a new world, it has to generate new chunks, and that will often cause stutters. If you move in any direction in that new world, it has to generate new chunks.
What would also help is knowing how much CPU and GPU percentage that task manager is reporting as well.