You can't purify a virus because you basically got to use eye of newt procedures to replicate the virus, meaning virus grow in and on cell cultures. You could never purify it, isolating it is when they successfully end up with what they took out of the host minus all the other stuff. You know what everything else looked like because you viewed those items singularly under a microscope, once you substract those buggers what's left is the virus. Yes it's totally possible after you succeed to doing that to make your own virus, even enhance that virus through gain of function research. That'd be when they isolate the virus they continue on until they break it down using similar eye of newt procedures. You could call it processes of elimination. Through lengthy processes you can learn how the virus operates, then you can throw in some bacon (figuratively) and see what it causes different parts of the virus to do. That's how they "gain" the function of a virus and that's most likely what they have done with this corona virus. See my latest Holy Shit Batman post.
Now you can purify a bacterium because they will grow just about anywhere the conditions are right, once you eliminate the source they grew on you have a "pure" bacterium, after that it's just a matter of what family they came from or is it a whole new family they are looking at.
Just as with bacterium having their own shapes the same will be found with viruses, if you repeat a process enough times and get the same results then that is the appearance of said bacteria or virus.