One way to hold this word: picture a bottle of black ink tipped over. Wherever the ink touches — a finger, a cuff, the edge of a page — it leaves a black mark that will not rub off. And if the ink covers the whole scene, nothing shows through it at all. Both uses of inky can be seen growing out of that one bottle: something has ink on it, or something is as black as the ink itself.
From the word’s history
The supplied entry derives inky from ink + -y, the ending that says 'having that quality', as in dusty or sleepy. So the word starts life meaning 'ink-ish', which is exactly where both uses sit.
來源把 inky 拆成 ink 加上 -y；-y 這個尾巴表示「帶有那種特質」，像 dusty、sleepy。所以這個字一開始就是「墨水感的」，兩個用法正好各站一邊：沾到墨水，或黑得像墨水。
Wiktionary entry for inky (adj), source_ref kaikki:3f6f69a190036ae4:1287845738, supplied in this packet