I'm writing a book and one character is Catholic and I'm not sure whether to use pastor or priest. And, one character gets possessed, yes I know that that's fictional, but would a Catholic "leader" perform an exorcism?
I will first answer the question posed by the O.P. in the title.
Priests vs. pastors
A priest is a baptized man (he has to be a male) who has received the second degree of the Sacrament of Holy Orders. That is, he was previously ordained a deacon (the first degree), and subsequently ordained a second time to the order of the presbyterate (the second degree).* (For this reason, a priest may also be called by the more technical name of “presbyter.” This term etymologically comes from the Greek “presbyteros”—that is, “older” or “elder.”)
Priestly ordination confers upon the ordained the capability of exercising certain functions that are necessary for Catholic worship: in particular the ability to celebrate Mass and confect the Eucharist. (He can also hear confessions, give the Anointing of the Sick, and, in some restricted but fairly frequent cases, give the Sacrament of Confirmation.)
(For an overview of the Church’s teachings on the presbyterate, or priesthood, see Catechism of the Catholic Church [CCC] Nos. 1562-1568.)
On the other hand, a pastor is simply the priest (or in a small number of cases, the bishop) who is in charge of a parish. As the Code of Canon Law (CIC) succinctly puts it,
A parish is a certain community of the Christian faithful stably constituted in a particular church [i.e., a diocese or similar structure], whose pastoral care is entrusted to a pastor (parochus) as its proper pastor (pastor) [probably better rendered “shepherd”] under the authority of the diocesan bishop.
(For the benefit of those not familiar with the Catholic Church’s organization, parishes are usually territorial—that is, they occupy a geographical area, usually a relatively small area within one city or town—and are typically associated with a single church, called the parish church. Some parishes may support several church buildings.)
In summary: priests are those baptized men that have been admitted to the presbyterate—that is, the second degree of Holy Orders. Those priests that have been chosen as the permanent heads of parishes—that is, the smallest territorial division of the Church—are called pastors.**
Applied to exorcism
When a man receives presbyteral ordination, in addition to the capacity to effect certain sacraments, it also gives him the power to perform certain sacramentals, including solemn exorcism. Nevertheless, he can only perform this kind of exorcism with the explicit permission of his bishop. As the Catechism explains,
The solemn exorcism, called “a major exorcism,” can be performed only by a priest and with the permission of the bishop. The priest must proceed with prudence, strictly observing the rules established by the Church (CCC 1673).
Hence, any priest—pastor or otherwise—could, in theory, be called to do a solemn exorcism (provided, of course, he has the necessary permission). However, the general practice in dioceses nowadays is to appoint a full-time exorcist who is an expert in these matters.
(Someone who fears that he is possessed, or otherwise suffering from demonic influence, would probably talk first with the pastor or another priest. This priest, in turn, would most likely direct him to contact his local diocese, who would then put him in contact with the exorcist, if necessary.)
* It is technically possible for a layperson to be ordained a priest per saltum—that is, without passing through the diaconate. However, such an ordination would be contrary to Canon Law (see Can. 1031) and the longstanding traditions of every apostolic church.
** There are a few complications that can be mentioned in passing. First, a handful of parishes are personal; that is, they are not associated with a geographical area, but comprise a groups of persons who have freely chosen to become members of that parish. Second, when the post of pastor becomes vacant, the diocesan bishop or ordinary will temporarily appoint an administrator, who has most, but not all, of the faculties of a pastor.
For your book, I believe it would be more accurate to employ the term that best suits the needs of your manuscript. In other words, if the exorcist priest is a Parish Priest, then yes he is a Pastor. But in everyday life, Catholics simply call their pastors Father "N."
Some Parish Priests are called Monsignor, if this title has been accorded to a priest by the Pope. In this case, a Catholic would address their pastor as Monsignor "N."
As Peter Turner points out in his excellent answer, priests may perform many functions within the Church such teaching in a seminary, chaplains in hospitals, prisons or some other institutions, etc. A priest exorcist may be chosen by the diocesan bishop from any one of these priests. I personally know of some exorcist priests who are Parish Priests (Pastors), one who is a professor from a Catholic seminary as well as one diocesan bishop (now retired) who has performed some exorcisms.
I grew up calling our parish priest (or pastor), quite simply Father "N."
In the Roman Catholic Church, a parish (Latin: parochus) is a stable community of the faithful within a Particular Church, whose pastoral care has been entrusted to a parish priest (Latin: pastor), under the authority of the diocesan bishop. It is the lowest ecclesiastical subdivision in the Catholic episcopal polity, and the primary constituent unit of a diocese. In the 1983 Code of Canon Law, parishes are constituted under cc. 515–552, entitled "Parishes, Pastors, and Parochial Vicars."
In American usage, a "parish priest" is any priest assigned to a parish even in a subordinate capacity, and some may be designated as associate pastors or assistant pastors. Globally they may be known as assistant priests, parochial vicars or curates. - Catholic Church Parish (Wikipedia)
To a Catholic a pastor is a priest who shepherds a flock (metaphorically speaking). There are many jobs for priests. They can be lawyers, teachers, scientists and probably other things that I can't think of now.
Exorcism requires special faculties (permissions and training) granted by the local ordinary (which is the Bishop who is the boss of the priests in the area usually)
Canon 1172 of the Code of Canon Law states that no one can legitimately perform exorcisms over the possessed unless he has obtained special and express permission from the local Ordinary, and states that this permission should be granted by the local Ordinary only to priests who are endowed with piety, knowledge, prudence and integrity of life. Cardinal Josef Ratzinger - Letter to Ordinaries regarding norms on Exorcism - 1985
So, I know at one pastor (i.e. a priest with a parish) who is in the process of performing an exorcism. It seems to be a very laborious effort that takes place over the course of many, many meetings (not too glamorous for a novel).
For a real depiction of what an exorcist does, I'd suggest picking up books by Fr. Gabriele Amorth from Ignatius Press.
But, to your question directly, you should be able to call your character a pastor. A Catholic "Leader", i.e. a Bishop or a Cardinal or the Pope, probably would not be one who would be an exorcist. But they (Bishops at least) would be involved in exorcism to the point where it seems likely that a priest who was to perform an exorcism would need the bishop's permission to do so.