Definition #1 for vieja
1- an old lady or to be old, but not derogatory if used in dimunative form.
2- a vulgar woman, a heffer.
2- your lady or girlfriend.

Example: 1- La viejita toda via le hecha ganas.
2- Mira esa vieja con el escote tan bajo!!
3- Yo y mi vieja nos vamos a dar unas vaccaciones a San Felipe...

Definition #2 for vieja
a term of endearment for your mother.
Could also be a nickname for a friend. Denotes that the relationship is old, not the person.

Example: La vieja makes the best pozole.
Hey vieja, quieres ir a la mall?
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