I didn't know, so I asked my sister, who teaches catechism. She thought they'd just use one and advised that I look it up in the Catechism of the Catholic Church. In its section on baptism, "anointing of the holy chrism" is used to describe the anointing at baptism.
Next, I asked my mother, who became Catholic as an adult. She's pretty sure she was anointed with both the oil of catechumens and chrism when she received the sacrament of initiation into the church (baptism, confirmation, and receiving the Eucharist) during Easter Vigil, but said she'll check her notes for me later today to be sure.
Anyhow, here's a digression on holy oil. Please comment with any corrections and/or clarifications as I assembled most of the following between rereading parts of the Catechism and relevant articles in the Catholic Encyclopedia.
In the Catholic faith, there are three specific types of holy oil: chrism, the oil of catechumens and the oil of the sick. All three are made from olive oil, although other plant oils may be used when olive oil is unavailable, and are blessed by a bishop during the Mass of the Chrism, which occurs on Holy Thursday.
In the order they're blessed during the Mass:
The oil of catechumens is used at baptism. A catechumen is someone that is receiving instruction in the faith but has not yet been baptized.
The oil of the sick is used for the anointing of the sick, also known as Extreme Unction or Last Rites.
Chrism is scented with balsam, which sets it apart from the other two holy oils. It is used in the sacraments of Confirmation and Holy Orders (ordination) and the consecration of objects, specifically churches, altars, vessels that come in contact with the Eucharist, bells and baptismal water.