An exhausted character can't be exerted. A character with more than 1 vitality can.
As for why some cards are written one way or another, I can't give you a satisfactory answer about why Decipher did much of anything. Why does
Dwarven Heart say "up to 2 times?" Its text is only effective after the condition is played, so all it does is allow a player to elect not to heal his Dwarf.
Task Was Not Done allows a player to discard "up to 2 minions," but how often would a player want to keep a minion on the table? This is the effect, again, so "up to" is trivial here.
HtGG can be used to heal himself once and discard a copy from hand to heal him again, for example.
If I had to guess, I'd say "exert a companion up to 2 times" is clunkier than "exert a companion twice." As I'm sure you know, I am
not going to argue that Decipher meant "up to" and said "twice." I don't think that is altogether relevant, either. I just don't see any reason to believe that if the card doesn't choose between two effects, applying an effect twice is any different from applying an effect up to 2 times to the same target.
I could ask you similar questions which, I believe, are even harder to answer. Why do the rules say "If the effect of a card or special ability requires you to choose one of
two different actions ..." rather than "one of several different actions ..."? Why does it say "one of two
different actions ..." rather than simply "one of two actions ..."? After all, if the common argument is true and choosing between different targets is choosing different actions, when is a choice between actions ever between two similar actions?
Merrick brought up an excellent point in the game hall that I want to address concerning step 6 of the "playing a card" sequence:
Perform effects of The Card. This includes choosing cards to be affected, if necessary. If initiative is a requirement for an effect, you cannot count The Card. If an effect takes a card into your hand from your discard pile, The Card is not there yet.
According to this, isn't "choosing cards" part of the effect, therefore choosing one card is a different effect than choosing another? I don't think so. I believe choosing a card is part of
performing the effect, but the effect itself (exert, wound, heal, discard, etc.) remains unaltered.
I do appreciate that this goes against what has been LotR TCG canon for potentially 15 years, and I think any opposition is reasonable. But if I apply the rules here with the same scrutiny that I apply the rules in any other scenario, I can't arrive at the old conclusion any more.
Interestingly enough, Zorbec's and the "Game Text:" section of the wiki say "you may spot an ally whose home is site 3 to heal that ally
twice." Presumably, that means that some source used to have that as the game text. Why was it revised? I don't think it's relevant, but maybe it's something to consider.