The main difference is that a TIA only lasts a few minutes. The clot then gets pushed along, like a temporary clog in a pipe, or chemicals in your body quickly break it down. Normal blood flow returns to your brain before any lasting problems set in. Symptoms can last for up to 24 hours, but they're usually gone in an hour.
Strokes, on the other hand, don't go away so quickly. That means some part of your brain goes without oxygen, and the longer that lasts, the more damage happens.