Here's how I use them, if I'm giving someone directions:
La stanga: to the left/[turn] left.
- Ia prima/a doua la stânga = take the first/second left
Pe stânga: on the left (side).
- e a doua casă pe stânga = it's the second house on the left
So basically "la stânga" would be which way to go, and "pe stânga" is which side of the road to look at when you're already at your destination or very close to it.