Striving is like trying. When you try, you put effort into whatever you're doing and then stop. Thus the phrase, "Try, try again". When you strive to do something, you put 110% into the task and you keep going until you either accomplish it or you confirm that what you're trying to do is impossible.
Dave: I tried... I really did. I just can't stay sober.
Mindy: Dave, it's because you're only trying. You're not giving it your all. You should be striving to stay sober, not just trying.
Marcus: I couldn't beat him! I keep trying to win, and he keeps rubbing my face in my efforts!
Bryce: Dude, you gotta be striving to win. You can't win by just trying - he's got skills, man - you gotta think above that. You know, you just gotta know you know you're gonna win, you know?
Marcus: At least I'm trying.
Bryce: Nah, I don't like that game, dude.