It's interesting as there are some coin toss options that would never make sense. For example, consider this hypothetical between the Patriots and Dolts, in which the Pats win the toss. Belichick (actually Matt Slater) can then, as you said, elect any of the following options:
a.) Receive
b.) Kick off
c.) defend side a or side b
d.) Defer
There is never any reason to select (b) or (c), as then the Pats would basically be handing the Dolts another possession. Basically, if a team wins the toss and elects to kick off, the losing team would then use their option to elect to receive to start the second half. Similarly, if the winning team selects an end to defend, the losing team could elect to receive to start the first half. Then, they make the selection all over again in the second half, the Dolts would get first dibs to start the 2nd half (having lost the initial toss), and would elect to receive again. I guess if the weather was really bad, it may make sense to sacrifice a possession in favor of wind direction.
What the Pats often do is simply defer, which basically forces the losing team to receive the opening kick. The Pats then inform the officials at the start of the second half that they will receive the second half kick. Technically, they could make a different selection, but that would be giving up a possession.
In OT, no team really "defers". In the regular season, there is only one OT period. A winning team could elect to pick an end zone to defend; the losing team could theoretically elect to kick off, but under current rules that would be really dumb. So in the case of that Pats/Jets game, Belichick did not actually defer; he instead chose an endzone to defend, which is justifiable in some (rather rare) cases.
In the playoffs, the only difference is that there is the possibility of a new kickoff to open the 3rd OT period. This is very rare; I think there have been less than 5 in all of the history of the NFL. But basically, the same rules apply; the team losing the OT toss gets the first choice to start the 3rd OT period. So, while a coach could defer, the chances of a 3rd OT period under the current rules are so small that it's extremely unlikely. And there is a new coin flip between the 4th and 5th OT period if the game is still undecided.