First, you're suddenly responsible for accuracy. Any time you solve a problem as an undergraduate and your results don't come out quite right, you get credit for explaining away what doesn't make sense. You can blame it on the temperature of the room or curvature of the earth or bad equipment or whatever and don't have to actually calculate anything, you just write and try to use big words to sound very technical and scientific. After graduation, you're suddenly faced with the idea that anomolies can't just be explained away. You have to take everything into account and understand everything that's going on.
The second big difference is that you're supposed to work on new and different problems, you don't do experiments to find out how fast gravity makes things accelerate or how much current flows through a circuit with a 1K resistor and a 5V source. These facts are known. You're expected to present something new and interesting to the world.
All this thinking is, In some ways, a pain in the ass. In others, it's pretty cool. Either way it really makes me wonder why I spent the first 22 years of my life not doing any of this. I sort of did it in senior design. But there's not really any reason that it couldn't have started before then. In high school I got horrible grades on english papers where I tried to form my own conclusions without quoting sources who'd thought of the conclusions before I did. In math classes our word problems were always carefully lined up with the chapter we were studying so it'd be obvious which method we were supposed to use to solve them. We just kill off creativity, we're like trained monkeys trying to guess what teachers want. I guess there are "enrichment" programs in some schools where the special gifted children are encouraged to branch out and think higher, but they're reserved for a small group... I was only gifted for a few years in elementary school, then we moved to a new school district where I was ruled "average", kept out of advanced math, and shown career test results that told me I'd make a great bus driver someday.
So taking that into account, graduate school is yet another one of those things that I look at and think, "I'm glad I didn't screw up and miss out on this. I hope I'm not screwing up and missing out on something else."