Английское dame означает "баба", но в русский оно вошло как дама, леди. Почему такое расхождение в оттенках?

В немецком Dame означает как раз "дама, леди". И во
французском тоже.
В классическом английском это слово НЕ означает
"баба", а как раз наоборот: леди, баронесса, госпожа.
В современном разговорном и в сленге приобрело
насмешливый оттенок: тётка, бабёнка.

это у американского сброда Dame превратилось в "бабенку" или "дамочку".

задолго до них слово Dame было титулом жены баронета или рыцаря.

в оксфордском словаре я даже не нашел уничижительного значения этого слова (есть только по созвучию с damn):

dame
1: I. Expressing relation or function.
A female ruler, superior or head: = ‘lady’, as fem. of lord (‘our most gracious Sovereign Lady, Queen Victoria’); the superior of a nunnery, an abbess, prioress, etc.; spec. the title given to Benedictine nuns who have made their solemn profession (cf. Dan1, Dom
; also, any fully professed nun. Also fig. or transf.
a. The ‘lady’ of the house, the mistress of a household, a housewife. Now arch. or dial. (my dame = my wife, my ‘missus’), or humorously applied to an aged housewife. b. transf. c. A girl; a woman. Chiefly U.S. slang. Also dial. (see E.D.D.). d. In modern pantomime, a comic character, that of a middle-aged woman, traditionally played by a man.
The mistress of a private elementary school for children. (Usually an old woman or widow.) Now almost Obs.
At Eton: A matron who keeps a boarding-house for boys at the school. (Also applied to a man who does the same.) II. Expressing rank or honour.
A form of address originally used to a lady of rank, or a woman of position; the feminine corresponding to Sire; = My lady, Madam: gradually extended to women of lower rank, and, after the 16th c., left to these (cf. sense 2, 6c). †
a. Prefixed as a title to the name of a lady or woman of rank; = Lady, Mistress, Miss. Now only fig. in personifications, as Dame Fortune, Dame Nature. b. The legal title prefixed to the name and surname of the wife of a knight or baronet, for which Lady prefixed to the surname is in common use. c. Prefixed to the surname of a housewife, an elderly matron or schoolmistress. arch. or dial.
a. The wife or daughter of a lord; a woman of rank, a lady. Now historical or poetic. b. A woman in rank next below a lady: the wife of a knight, squire, citizen, yeoman. arch. or dial. c. The title of female members of the Primrose League of the same rank as the ‘knights’. d. The title of women members of the Order of the British Empire; also Dame Commander, Dame Grand Cross. III. A mother; = dam n.2 †
A mother. Obs. a. of human beings. b. of animals; = dam n.2
IV. †
The queen at chess. [= F. dame.] Obs. rare. V.
Comb., as dame-errant (nonce-wd. after knight-errant); dame-school (also dame's school), an elementary school for children kept by a dame.
2: obs. f. dam n.1 and n.4, and damn.

Зато русское Баба, вошло туда как Бэйб - крошка))

возможно, это слово пришло не оттуда