I think that the "total reputation" tab sorts the user basing on the sum of reputation in all the sites where the user has an account (and the reputation is at least 200), while the "user reputation" sort the users basing on the reputation they have in the six sites where their reputation is higher. Users without an account with a reputation of at least 200, or with a single account where their reputation is at least 200, are handled differently.
(The accounts shown in the screenshot are Mohit Bumb, and Simon Hodgson.)
To notice that in the case of, he has more than 2 accounts, and the sum of the reputation on those accounts is higher than 202. This could be explained with cached data that is used to show the flair, but it could also be explained with the fact the flair doesn't show the sum of the reputation on all the sites where the user has an account. Knowing which sites are considered, in this case, is quite difficult; I would expect that Area 51 is always included, but I cannot confirm this.
Taking as example Pearsonartphoto, 29129 is the sum of 10717, 6274, 1482, 1172, and 1137; 31449 is the sum of those six numbers, and the reputation he has in other 13 sites.
Normally, there is no difference between sorting the user using their total reputation, or their user reputation. In some cases, there could be a difference, such as in the following (hypothetical) example:
Site User A User B
Site A 20240 20000
Site B 20000 20000
Site C 15000 15240
Site D 12500 12560
Site E 11060 11000
Site F 10000 10000
Site G 0 5600
Site H 0 5800
Site K 0 4800
The total reputation for User A is 88800, while for User B is 105000; the user reputation for both is 88800.
For users that have referred other users, I think the total reputation includes also the reputation of the referred users, such as in this case: