You can specify effects as either "REPEATED" or "RANDOM" and what this basically means is the following. The mixed model is just as you wrote it, where b is the vector of fixed effects, u is the vector of random effects, and e is the vector of errors. The conventional notation is to let G be the covariance matrix of u, and let R be the covariance matrix of e. You may have heard the phrases "G-side covariance structure" or "R-side covariance structure" and this is what these refer to. When you specify an effect as RANDOM, you are modifying the matrix G, either by letting some of the diagonal elements (i.e., the random effects) have some non-zero variance to be estimated, or letting some of the off-diagonal elements (i.e., covariance between random effects) have some non-zero value to be estimated, or whatever. When you specify an effect as REPEATED, you are instead modifying the matrix R, that is, you are allowing the errors to be correlated in some way, for example by estimating a block covariance structure such that errors from the same subject are potentially correlated while errors from different subjects are uncorrelated. In certain simple cases you can get the same substantive answer either way (e.g., by adding subject-level random effects or adding non-zero correlations between errors for a given subject), but they are not the same in general. Hopefully this is not too confusing.