There are several saints named Teresa. To answer your question correctly, you need to be more specific.
St. Teresa Redi is a saint but not a patron saint.
She became St. Teresa Benedicta of the Cross.
St. Teresa of Jesus also known as St. Teresa of Avila was born in Spain.
Mother Teresa's patron saint was St. Therese of Lisieux.
Mother Teresa has not yet been declared a saint. She has been beatified, however.
St. Ignacious of Loyola
There are a number of saints named Teresa. Please be specific.
Yes, Saint Teresa and Saint Thérèse of Lisieux are different saints. Saint Teresa typically refers to Saint Teresa of Avila, a Spanish mystic and Doctor of the Church, while Saint Thérèse of Lisieux, also known as "The Little Flower," is a French Carmelite nun and Doctor of the Church. Both are highly regarded for their spiritual writings and devotion to God.
According to the Patron Saint Index the patron saints for vocations are St. Alphonsus Maria de Liguori and the Infant Jesus of Prague. There is no St. Teresa among them.
Mother Teresa has not yet been canonized as a saint and has only been beatified.
There are a number of saints named Teresa so you need to be more specific.
I have placed a link below of the biography of Teresa of Avila.