Hanging faux wood blinds- screw broken. Is there a tough screw I can use for a wall stud?
You said you pre-drilled but then said you thought you hit a stud with the screw?

Nope not if you pre-drilled.

If you did that properly and drilled all the way into what the depth of your screw would be, you would have drilled into that stud and the screw would go in just fine. The drill bit when you backed it out, you should have seen the pine wood on the bit flute : if it went into a stud. 

Perhaps you did not drill deep enough or maybe there is a metal protective plate - protecting pipes or wires. Further your drill bit could be a size to small for the screws.

Wood Screws are what you want - standard wood screws are fine - they go through studs just fine - pine is a VERY soft wood (of course that is relative - if some one hit me with one I probably would say it was hard enough). 

No there are no special screws just for studs.

When was your home built and did they use steel studs to build it ?