You can think of one picture holding all three uses: a figure tipping a jar so that water pours out. That figure was first traced in the stars, then borrowed as one of the twelve dated boxes of the zodiac, and finally used for the people whose birthdays fall in that box.
Latin aquarius means water carrier, from aqua (water) plus -arius; it is a straight rendering of Greek Hydrokhoos, the water pourer, and the figure traces back to depictions of the Mesopotamian god Ea with water pouring from his shoulders or vases.
拉丁文 aquārius 是「提水的人」：aqua（水）＋ -arius。它照著希臘文 Hydrokhóos（倒水者）直譯過來，而更早的人形，來自美索不達米亞的神 Ea——圖像上水從他的肩膀或瓶子流下。所以「倒水」這個畫面，是名字本身就帶著的，不是後人硬配的。
Wiktionary entry Aquarius, etymology_text supplied in packet (source_ref kaikki:3f6f69a190036ae4:453618457:42438)
Two branches
天上的星圖與黃道的那一格
這一支最靠近原本的畫面：先有天上那一片星星被看成提水的人，占星再把同一個名字拿去指一段日期。
noun · B1
The eleventh sign of the zodiac, drawn as a person pouring out water. People born between about 21 January and 19 February are said to be born under this sign, and some people believe it shapes their character and their life.
水瓶座
生在那一格的人
名字再往前走一步：從那一格日期，落到生日在那段日期裡的人身上。
noun · B1
A person who was born between about 21 January and 19 February, and so belongs to the sign Aquarius.
水瓶座的人