The second model states (more or less) that, for ordered IDs, the person-specific mean values follow an AR(1) structure. That is, suppose that you had 5 individuals who had the following ID's and mean values:
ID mean
243 18.21
129 18.96
141 19.44
227 26.33
313 22.71
Now, if we order this table by ID, we have
ID mean
129 18.96
141 19.44
227 26.33
243 18.21
313 22.71
The ordered mean values are 18.96, 19.44, 26.33, 18.21, and 22.71. There is a variance to these mean values. That is what the first of the three covariance parameters is estimating. The AR(1) parameter is estimating a covariance structure in which individuals who have closer ID values would have stronger covariance of the mean values - an assumption that I doubt you want to make. The last of the three covariance parameters, the residual variance, is estimating the variability of person-specific values about their mean values.