Why do BH3 and NaBH4 have different selectivities?
Your assertions are correct, for the most part. $\ce{BH3}$ is a Lewis acid, and it does not reduce carbonyl groups by directly donating a hydride group like $\ce{NaBH4}$ does. The $\ce{NaBH4}$ reduction mechanism is fairly short and involves a direct transfer of the a hydride ion to an electron deficient carbonyl carbon:

$\hspace{2.4cm}$

$\ce{NaBH4}$ is incapable of reducing carboxylic acids only because the acidic hydrogen is more reactive towards the hydride ion than is the carbonyl carbon. It is, in fact, capable of reducing carboxylate anions to primary alcohols, though the reaction is very slow. Electron-rich carbonyls favor reactions with electrophilic reducing agents. To help in understanding what makes a carbonyl electron-deficient or rich, let us consider the contributing resonance structures of amides, esters, and acid chlorides:

$\hspace{4.7cm}$

Nitrogen atoms are much better than bearing a positive charge than are oxygen than is chlorine. In this way, you can think of nitrogen donating its lone pair into the carbonyl the most, making it electron-rich, and the chloride donating its lone pairs the least, making it electron-deficient.



The $\ce{BH3}$ reduction mechanism is quite a bit longer and has some interesting intermediates, but here it is:

$\hspace{2cm}$

Note that this mechanism does in fact include hydride transfers (it has to). Though you were right in thinking that $\ce{BH3}$ wouldn't immediately donate a hydride, coordinating to a lone pair weakens the $\ce{B-H}$ bonds and makes hydride transfers possible. $\ce{BH3}$ and $\ce{NaBH4}$ really aren't as different as you might first think.

Though $\ce{BH3}$ is more reactive towards electron-rich carbonyls, it is also capable of reducing electron-deficient carbonyls like acid chlorides and esters through similar pathways. This should show you that there isn't any contradiction here, and that just because two compounds have different reactivities does not mean that they cannot perform the same type of reactions—they just won't perform it in the same way.