I'd think of the 'learning' aspect more of a... 'breaking it in' aspect, personally, as opposed to true sentience.

Example (again, my opinion only):

So in my own head canon, a witch or wizard who has a 'single, pure passion' or 'obsession' as a youngster might get this wand.

The wand 'learns' from its master in that it 'adapts' to their style of magic, which might be, say... quick and dirty spell-casting. Anyone else who tried to use this wand later, after it had 'learned' from its master, would get better results if their own style of casting matched what the wand had learned from its master.

Similarly the wizard might learn from the wand. While the initial match was made based on a single passion for a certain subject, the wizard might 'learn' from the wand in the sense that that passion is reinforced. As they use their wand to work towards their goal they are subtly learning dedication from synergy with their wand, and would therefore be less likely to deviate from their goals than another wizard. Or than they would be if they had bonded with another wand.

It's like if you have two puzzles pieces that almost fit together, but not quite... at least not until you rub them together over, and over, and over until they mesh perfectly. In a sense each piece will have adapted (or learned) to be a perfect fit for the other.