Hello Andy,
Both are verb "tener" which means " got, have got"
They are however different tenses with the third personal pronoun "Ella":
Tenía: pretérito imperfecto
Tuve: pretérito (indefinido)
So both are correct and represent a past event, but choosing either of them depends on the context of the sentence:
- Tenia :
(Pretérito imperfecto)
This tense is used to refer to a habit in the past like saying "used to".It is not connected to a certain event or specific timing in the past but is extended limitless. It refers also to habitual, repeated action.
Ella tenia un perro.
She "had", "used to have".
It implies that the action is past ,she doesn't have a dog anymore, yet no specific time is mentioned.
Tuve:
(pretérito (indefinido)
It is used when describing specific actions in the past and usually mentioning therefore when they happened, they are usually part of a chain of actions in the past.They refer to one time, completed action with a specified number of repetitions.
Ayer Iba a estudiar, pero no tuve tiempo.