Straight-edge people make a LIFETIME (this is key) commitment to abstain from drugs, alcohol, and drugs. It's different from saying "I'm only going to drink responsibly", but rather "I'm not going to sip a drop of alcohol for my entire life". Some SxEs get pretty uptight as well. Many times, they draw a "X" on their hands to represent themselves. Often, but not always, these are the people who think they're superior to others who do drink or smoke.
Not necessarily. If you simply don't drink or smoke, it does not mean you are Straight-edge. SxEs, as stated above, make commitments to never use these substances. If you don't smoke or drink because you happen to be underaged, or you just aren't into it, you're not a straight-edger. If you feel that it's 'wrong', morally or otherwise, then you may be one.