The right answer is: there is no difference between pollywogs and tadpoles. Even tadpoles with legs developing are still tadpoles - or pollywogs. Once the arms develop and they take on a more frogly shape, they leave the tadpole state to become froglets. At this point, they’ll still have stubs that were once their long tails.
Of course, there may be exceptions; if you’re from New Zealand or Australia, the term polliwog might even refer to young frogs that are fully developed. But that’s not the general definition. Some answers are way off base, so be forewarned when searching around the Internet’s question and answer sites.
The majority of tadpoles are amphibious, complete with gills. Over the course of a few days or weeks, drastic changes begin to take place. This makes them fascinating subjects for up-close study.
If you’re in an area where there’s plenty of fresh pond water, it’s fun to collect the tadpoles and watch them grow in a home habitat. In fact, you might be doing them a favor. When they’re so small, larger predators - with one gulp - can wipe out quite a few of them at once. Once they’ve matured, they can be re-released. More on raising tadpoles later.
And, by the way, their tails do not “fall off.” Instead, they just reduce in size as they’re reabsorbed into the frog’s body.
Photo: Public domain courtesy ShortBus