Mankins and so far all the rest (Ngata, Jackson, Woodley when it's announced) got the standard or non-exclusive tag. They are free to talk to other teams (once FA starts which will be a problem for them this year if there isn't any...) and if they are signed to an offer sheet the team has a week to match the offer or accept the prescribed compensation of two first round picks. In those cases the team decided either they weren't going to elicit that kind of compensation or they'd be just as glad to move on if they did... The difference in the two tags besides the inability to talk to potential suitors is the player gets the average of the top 5 salaries from this season and not last under the exclusive tag. Usually that is significantly higher, although this year without new FA contracts to fuel the calculation it might not be.
In Manning's case the $$$ difference was immaterial since his cap hit was so high last year he qualifies for 120% of his previous "salary" calculation which works out to $23.1M. His situation is unique though as in the last couple of years of his expiring deal his cap hits have been in excess of $20M anyway, he's 35 and counting, and for Irsay having the cap pay Manning's cost may be preferable to having to come up with cash over cap (bonus money) to craft a deal that would allow for lower caps early on at the expense of the backend of the deal (which may be coming sooner than later now). It's going to be tough enough sledding for Indy when he does go, let alone if they have massive dead cap to deal with for the first couple of post Manning years...
