And does the difference, if any, matter?
First, keep in mind that there are many expert sources on this subject and not all of them agree. Below is what I have found to be most consistent but that doesn't mean they are correct. I have provided external links in order to supplement your information further.
Vellum is made from calf and adult cow skins. When you scrape it to make corrections, when done correctly, there is no trace of the correction having been made.
Parchment is most commonly goat or sheep skin. The skin is split and then goes through pretty much the same process to make vellum. When you scrape it to make corrections it is fairly easy to tell that a correction has been made by a trained eye.
Today, the word parchment has come to mean (in general, not in all circumstances,) all animal skins used to write on and vellum is (generally,) considered a subcategory of parchment. Vellum is also, confusingly, known at times as the finer grade of skin regardless of what animal skin it is. However, to the best of my knowledge, only on calf and cow vellum can corrections be done without someone being able to detect it.
If you are making a project for beauty, then you will probably want to use vellum. If however you are attempting to collect taxes or put the title to your land on something, you might be more likely to put it on parchment. That way you have protection from someone modifying the document without being detected. In fact in England at one point all tax rolls were required by law to be put on parchment so that people couldn't bribe the tax collectors to charge them less than the tax they were supposed to pay.
As you can see the difference can matter.
Here are some links to other people's thoughts on parchment vs vellum. I provide these for the purpose of diversity of thought.
The National Archives - USA
Lochac College of Scribes - Parchment Making (see 5th paragraph)