Definitions without pictures - this should be interesting. =) A back tuck is a complete backward revolution of the body with the knees tucked to your chest, and your hands do NOT touch the ground. A back handspring is a 2-part movement (done consecutively). You first jump back, arch your body back to hit your hands on the ground behind you with arms overhead (it looks like a back bend at this point, except momentum has already carried your feet partway over), and then you snap your feet through a handstand and land. Here is a much better demo/definition: http://cheerleading.about.com/ library/faq/bl_backhandspring.htm? terms=gymnastics
I had good instruction. I also had two spotters the first time i did it. They had to catch me. haha. If you arent scared you wont have problems. If you just think about jumping as high as possible and then pulling your knees to your chest at the highest point youll flip around. Its not that simple but if you do that youll at least not land on your head. People on land on their heads when they freak out and open up early. Just dont freak and youll be fine.