I am a teacher, though not in Michigan -- do understand that things can be very different state to state. Here's what's true for me:
Pension: 10% of my paycheck goes into the teacher-and-state-employee pension fund (not a choice, pre-tax dollars). At the 5-year mark, I was vested in the pension plan, which meant that I was a full-fledged member. If I had left prior to the 5-year mark, my contributions would've been returned to me. After the 5-year mark, I am assured of being able to draw a benefit, though the longer I work, the higher that benefit will be. The formula for determining my benefit:
Average of my highest 4 years of salary X .0182 X my years of service
BUT that formula is only true if I either finish 30 years of service OR am 65 years old. If I retire earlier, the percentage that I receive goes down. If you're thinking about the two of you retiring when she's around the 5-year mark, she's going to get essentially nothing from the pension.
The pension is for the rest of the recipient's life, whether that's two years or fifty years, which is good because it means you cannot "outlive your money"; however, it's a STATE pension, which means you have to put in all my years in one state. And since some states are phasing out pensions, a person who takes a leave of absence might come back to find that he or she is no longer eligible for the pension program.
The rules for your girlfriend's pension are certainly written down and easily found online. It's important that you know the rules for YOUR OWN STATE and that you filter those rules through your own ideas for the future. Generally speaking, a pension is only a good deal for a person who puts in the full 30 years and "maxes out" the benefits.
401K: This is a personal retirement savings account. Your girlfriend can decide how much to put into the account, but she cannot pull out money until she's 59 1/2 (without paying a big penalty). The benefit is that it's pre-tax dollars. This is more flexible than a pension; the money is hers even if she changes jobs, moves out of state, or whatever. But she can outlive this money.
Social Security: You didn't mention this, but you need to know where she stands with Social Security. In some states, teachers do not pay into Social Security, which means they don't receive checks later; in my state, teachers pay into BOTH the pension fund AND Social Security, so we get checks from BOTH later. This can be a problem for teachers -- but, obviously, the right answer is awareness. I read something online some time back about a teacher who taught 10 years in State 1 /paid into SS for 10 ... then moved to State 2 /did NOT pay into SS for 20 years ... but she assumed that the 10 years she'd paid in was enough to get her a check ... no, SS entered 20 years of zeros for those years, meaning that she received almost nothing. I'm sure I didn't get those numbers right, but the point is valid.
Retirement is probably the best benefit teachers still have (so many benefits have dried up for us), but you need to understand the rules to make it work for you.