Plavix is used to reduce the risk of heart attacks and strokes, particularly in people with a recent history of stroke or heart attack, and those with peripheral vascular disease (peripheral artery disease, PAD).
Plavix/clopidogrel is mainly an anti-platelet drug (they are *usually* used artery-side, e.g., to prevent strokes or heart attacks). The other drugs mentioned are anticoagulants (which interfere with coagulant proteins such as Factor Xa -- they are usually used venous-side, e.g., preventing DVT after orthopedic surgery). Either type might be used for the in between, which is the heart: for AFib clotting/strokes.
I don't know why your doc preferred to prescribe Plavix for DVT. But prasugrel and ticlopidine are next generation drugs of the same kind as Plavix. Maybe they'd have fewer side effects than Plavix.
Another new anticoagulant (with a different MOA) that isn't so well known is based on... leech saliva! That makes sense :)
There are newer blood thinners that can be given in pill form without the need for an injectable blood thinner. These include rivaroxaban (Xarelto) and apixaban (Eliquis). You can discuss with your doctor.