Is there a difference between perfect collinearity and multicollinearity? I've read that for multiple regression analysis there is an assumption of no perfect collinearity. Is that the same as multicollinearity?

No. If your regressors are perfectly collinear, OLS estimation is impossible. In contrast, the more multicollinear (high collinearity but not perfect) your regressors the more inefficient your estimator, but OLS estimation under imperfect multicollinearity is very much possible and the OLS estimator is even consistent and unbiased. In your mind, you can usefully think of the effect of multicollinearity as that of decreasing your usable sample size.
