Well, the main difference was that on my own projects, I was the entire crew practically. Shooting for other directors and with crews is what I had to learn later in film school and afterwards -- the issue of collaboration, which wasn't so much of an issue when I did everything.
On my first feature with a budget, one of the things I forgot to think about was where equipment trucks could park. We picked a location on a narrow street in the Hollywood Hills and I had all the trucks in my way when we did our exterior shots (but there wasn't anywhere else to park). Now this was mostly my fault but looking back, I wonder why the more experienced (then) AD and Transpo Captain didn't think about it either. Now when I scout locations, I'm much more aware about trying to hide the crew, trucks, and gear from the camera angles. You have to know what will be on-camera and what will be off-camera. There is a huge apparatus to filmmaking that has to be dealt with.
Dealing with a tight schedule is another thing that has to be learned. Knowing how much you can shoot in a 12-hour day, etc.
As for making small films look bigger-budgeted, that's sort of what most decent cinematographers do. You have to find things that add production value in ways that don't take money to accomplish. It may be just a spectacular view from a hilltop, or great-looking location (or leading actress!) It's also understanding that most good lighting is SIMPLE, or at least, LOOKS simple, so it's not always about how much equipment you have but learning to put one light in the best place for the look you want.
When you have a tiny crew with almost no equipment, you have some advantages too -- you can move to different locations faster, you can wait for the natural light to be right, etc. When I was shooting Super-8 I had all sorts of tricks to get great shots, sometimes just by noting locations around LA that looked photographically interesting, like "hey, there's a bus bench under this freeway overpass; a person sitting on this in silhouette against a bright background on a telephoto lens would look very striking..."