What is a secular priest ?
A priest who works for the Arch/Diocese. Not affilitated with any religious order.
The other type of priest is a reigious priest if he belongs to a religious order like the Dominicans or the Spiritans etc.
Actually, some so-called “religious orders” are not religious orders at all. The Church calls them “apostolic life communities”. They are secular priests who live in community. The Paulists, the Maryknoll Fathers, the Patricians, the Oratorians make up this group.
I suspect what the person using the term “secular” meant was diocesan; i.e. the priest is directly under the authority of the bishop and does not belong an order. As the wag said, he doesn’t take the vow of poverty; he just lives it!