A savant can be pictured as a person named by what they know. Someone has gone much further into one thing than the people around them, and is now the person you go to when the question is hard. In the first sense that depth is spread across a whole subject and built up by years of study. In the second sense the same depth is squeezed into one narrow point, such as dates, numbers, or a tune heard once, while the rest of daily life stays difficult. Both uses point at the same shape: knowing one thing the way almost nobody else does.
From the word’s history
Borrowed from French savant 'one who knows', from Latin sapiō 'to know, to have judgement'; English sapient is a doublet. The second sense is a clipping of the older phrase idiot savant, literally 'wise fool'.
savant 借自法文 savant（懂得的人），再往上接到拉丁文 sapiō（知道、有判斷力），英文的 sapient 跟它同源。第二個意思不是從「博學」一路引申的，而是從舊說法 idiot savant（字面「有學問的笨蛋」）切短下來的。
Wiktionary entry supplied in this packet (source_ref kaikki:3f6f69a190036ae4:588746609)
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