Elder is an official position different from that of a priest. It should be noted that every most elders are also a priest (they are still a priest after becoming an elder). A priest is usually ordained an elder after 1 year or when the priest turns 18, if all gos wells.
The office of priest is an office in the Aaronic Priesthood. The office of elder is an office in the Melchizedek Priesthood (which is an extension of the Aaronic Priesthood).
Here are the duties of a priest (D&C 20:46-52)
46 The priest’s duty is to preach, teach, expound, exhort, and
baptize, and administer the sacrament,
47 And visit the house of each member, and exhort them to pray vocally
and in secret and attend to all family duties.
48 And he may also ordain other priests, teachers, and deacons.
49 And he is to take the lead of meetings when there is no elder
present;
50 But when there is an elder present, he is only to preach, teach,
expound, exhort, and baptize,
51 And visit the house of each member, exhorting them to pray vocally
and in secret and attend to all family duties.
52 In all these duties the priest is to assist the elder if occasion
requires.
Here are the duties of an elder (D&C 20:38-45)
38 The duty of the elders, priests, teachers, deacons, and members of
the church of Christ—An apostle is an elder, and it is his calling to
baptize;
39 And to ordain other elders, priests, teachers, and deacons;
40 And to administer bread and wine—the emblems of the flesh and blood
of Christ—
41 And to confirm those who are baptized into the church, by the
laying on of hands for the baptism of fire and the Holy Ghost,
according to the scriptures;
42 And to teach, expound, exhort, baptize, and watch over the church;
43 And to confirm the church by the laying on of the hands, and the
giving of the Holy Ghost;
44 And to take the lead of all meetings.
45 The elders are to conduct the meetings as they are led by the Holy
Ghost, according to the commandments and revelations of God.
A worthy priest can baptize, confer the Aaronic priesthood and ordain men to offices in the Aaronic priesthood and participate in any position in the sacrament.
A worthy elder can bestow the gift of the holy ghost (after someone is baptized), confer the Melchizedek priesthood, ordain men to the office of elder in the Melchizedek priesthood, give priesthood blessings and consecrate and/or dedicate oil, graves, and homes, as well as do anything a priest can do.
They are both are bound by the Covenant of the Priesthood. Elders are also bound the oath.
Also certain elders use the term "Elder" as a title (for example, general authorities and missionaries). Most elders do not though, but are still elders.
