
die Mutter
mother
The female person who has given birth to or adopted a child and raises it.
Meine Mutter kommt am Wochenende zu Besuch.
My mother is coming to visit this weekend.
mother / nut
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mother
The female person who has given birth to or adopted a child and raises it.
Meine Mutter kommt am Wochenende zu Besuch.
My mother is coming to visit this weekend.

nut
A small metal piece with an internal thread that is screwed onto a screw or bolt as its counterpart in order to fasten something.
Für diese Schraube brauche ich eine M8-Mutter.
I need an M8 nut for this screw.

source / origin
In a figurative sense, the source or origin of something. Often used in fixed expressions like "die Mutter aller Schlachten" (the mother of all battles).
Man sagt, die Not sei die Mutter der Erfindung.
They say necessity is the mother of invention.
The meaning of 'Mutter' (mother / nut) depends heavily on the context. In a family setting, it is the female parent. In a technical context, often together with 'Schraube' (screw), it refers to a metal part.
Seine Mutter ist eine bekannte Ärztin.
His mother is a well-known doctor.
'Mutter' (mother) is the base word for many important terms. These include, for example, 'Muttersprache' (native language, the first language one learns) or 'Schwiegermutter' (mother-in-law, the mother of one's spouse).
Deutsch ist nicht meine Muttersprache.
German is not my native language.
In connection with family, there are fixed expressions. 'Mutter werden' means to become a mother, and a 'werdende Mutter' is a pregnant woman.
Meine ältere Schwester wird bald Mutter.
My older sister will soon become a mother.
The figurative meaning 'Ursprung' (origin) is used almost only in fixed idioms and proverbs. A very well-known one is: 'Die Not ist die Mutter der Erfindung' (necessity is the mother of invention).
Diese Niederlage wurde später als „die Mutter aller Krisen“ bezeichnet.
This defeat was later described as 'the mother of all crises.'
source
Both words can refer to the source or trigger of something. “Die Mutter” is a figurative, often personifying expression, while “die Quelle” sounds more neutral and factual. Use “Mutter” for a strong rhetorical effect and “Quelle” for a matter-of-fact statement.

Der Hass gilt als die Mutter vieler späterer Konflikte.
Hatred is considered the mother of many later conflicts.
Der Hass war die Quelle vieler späterer Konflikte.
Hatred was the source of many later conflicts.