I think a weapon is Martial when it is supposed to be part of common training for martial characters (the ones who belong to armies, guard groups, paladins orders...).
Usually I imagine that a character which has proficiency in all martial weapons, has been trained in (1) the use of weapons in general and (2) the use of most weapons available to a typical army or fighting group. For instance, it's possible that one fighter might have never used a guisarme, but his training with polearms is so solid that he could use one proficiently the first time.
A weapon is exotic when it has something unusual so a general training with weapons isn't enough, and you need some extra training to get familiar with it: it could be because the weapon has a peculiar shape or way of use, like a spiked chain or a whip.
Sometimes weapons are exotic just because of their foreign origin, and they could be martial in a different setting or just for a different group of warriors (see weapon familiarity, it just means that!).
So IMO when it comes to bows, they may be more difficult to learn (in terms of time required for the basics) than a greatclub or a warhammer, but they are still part of the general training of every martial class because they are the standard ranged weapon in armies etc. You don't need to specify if the Fighter needed to spend a year to learn the bow and a month to learn the warhammer, in one way or the other he knows both after his 1st level training.
For non-martial characters there is no difference if a weapon is martial or exotic. In either case it takes a feat to learn to use it.