One way to hold this word: something soft and thirsty is pressed on a surface and wiped along it, and whatever was there comes away on it. Size is the only thing that changes. Make it huge and put it on a long stick, and you are washing a wet deck. Shrink it to a finger's width of cotton, and you are cleaning a cut or touching the inside of a cheek. What comes away can be dirt, water, or a tiny amount of something a lab wants to look at.
The evidence packet dates the word to the mid 17th century in the sense 'mop for cleaning the decks'. It is a back-formation from Middle English swabber, a sailor whose job was to swab decks, from Middle Dutch zwabber, on a Germanic base meaning 'splash' or 'sway'. So the deck mop came first, and the small cotton stick is the same tool made tiny.
依證據包所附的字源，這個字十七世紀中期先指「刷洗甲板的拖把」，是從中古英文 swabber（負責刷甲板的水手）倒推出來的名詞，再往前是中古荷蘭文 zwabber，源頭那個日耳曼語詞根帶著「潑濺、甩動」的意思。也就是說，船上的大拖把在前，診所那支小棉棒在後：同一件工具縮小了，動作沒變。
Wiktionary entry for 'swab' (etymology_text supplied in this evidence packet; source_ref kaikki:3f6f69a190036ae4:815217034)
Two branches
一小塊沾取、擦拭用的軟材料
這一組是核心畫面縮到最小的樣子：軟材料只有指頭大，動作也只有輕輕一抹。因為範圍小，它就能進到身體裡、進到細管子裡，做拖把做不到的事。
noun · B2
A small piece of soft material, usually cotton on the end of a thin stick, that you use to clean a wound, put medicine on skin, or take a tiny amount of something from a person's body so it can be tested.
棉棒／拭子
船上的拖把與大水刷洗
同一個畫面放到最大：軟材料變成長棍前端的濕布，地面先淋上一大片水，再來回推。這是這個字最早的樣子，其他意思都是從這裡縮小出去的。
noun · C1
A mop, especially one kept on a ship for washing the deck.
拖把（多指船上）