JOEL - I will provide definitions for each term according to scripture and latter-day revelations to LDS church prophets. (D&C = Doctrine and Covenants)

Revelation:
Revelation is the process by which God communicates to man. It can be by way of personal communication from God to a single individual who is seeking His council and inspiration, or it can take the form of direct verbal or visual communication between God and His prophets to reveal a specific doctrinal truth or commandment that God wishes all of His children to know about.
Revelations can occur in several forms. They can come by way of visions(Acts 7:55-60, D&C 76); direct verbal communications with God or angels(Ex 3:2-4); by dreams(Gen. 20:3,6, Gen. 31:11,24) ; by way of the still small voice from the Holy Ghost(1 Kings. 19); or by having a burning in the bosom as an indication of the will of God(D&C 9:8).
Everyone is entitled to personal revelation concerning their own lives or the lives of their families. Those in leadership positions in the church can receive revelation in regards to their responsibilities in performing their duties.
The LDS prophet Joseph Smith taught us how to recognize and receive revelation:
"A person may profit by noticing the first intimation of the spirit of revelation; for instance, when you feel pure intelligence flowing into you, it may give you sudden strokes of ideas, so that by noticing it, you may find it fulfilled the same day or soon; (i.e.) those things that were presented unto your minds by the Spirit of God, will come to pass; and thus by learning the Spirit of God and understanding it, you may grow into the principle of revelation, until you become perfect in Christ Jesus [Teachings of Prophet Joseph Smith, p. 151].
The President of the LDS church is the only one who can and will receive revelation from God in regards to church doctrine and practices.

Apocalypse:
Apocalypse is a Greek word which means "revelation". It usually refers to the writings of prophets such as Isaiah, Daniel, and the New Testament Revelation of John. Apocalyptic literature usually contains autobiographical information of the writer; reports of visions; descriptions of heaven; revealed teachings or doctrine; and prophesies of future events.

Rapture:
"Rapture" refers to a supernatural event where, according to many born again traditional Christians, they will suddenly disappear from the earth and be taken by Jesus to heaven.
The term "Rapture" is translated from the Greek (harpazo) and Latin (Rapere) bible texts meaning "to snatch" or "take away".
The apostle Paul wrote to the Thessalonian Saints that those living on the earth at the time of Christ's appearing would be "caught up" to meet him (1 Thess. 4:16-17, Mat. 24:40-41).
LDS doctrine does not call it "Rapture" but describes the same event where the righteous saints will be "quickened" and will join those "who have slept in their graves," who will also "be caught up to meet him in the midst of the pillar of heaven" (D&C 88:96-97)
According to LDS scripture, following the rapture, the wicked will not destroy each other. Jesus will cleanse the earth by fire and destroy all the wicked Himself.
"And every corruptible thing, both of man, or of the beasts of the field, or of the fowls of the heavens, or of the fish of the sea, that dwells upon all the face of the earth, shall be consumed;
And also that of element shall melt with fervent heat; and all things shall become new, that my knowledge and glory may dwell upon all the earth."(D&C 101:25-25)
Following this will begin the Millennial reign of Jesus on the earth with His righteous resurrected saints for a thousand years.