Some people use "apostles" and "disciples" interchangeably when talking about the 12 that originally followed Jesus. Yet, I don't commonly hear the opposite, people using those two words interchangeably when talking about those that follow Jesus after his resurrection and ascension. When I do hear them interchanged, it doesn't sound correct. What is the difference between an apostle and disciple? And does it change from denomination to denomination?
The Catholic Encyclopedia, New Advent, defines the terms as follows:
Besides the signification of "Apostle" and that of "believer" there is finally a third one, found in St. Luke, and perhaps also in the other Evangelists. St. Luke narrates (6:13) that Jesus "called unto him his disciples, and he chose twelve of them (whom also he named apostles)"
This is just an excerpt. The article discusses the definition of the term in length and goes over each of these three-ish usages.
The term Apostle also has three-ish usages, but two chief usages. One is as a Greek translation of the Aramaic title Jesus gave the twelve: seliah.
This word means:
"those who were despatched from the mother city by the rulers of the race on any foreign mission, especially such as were charged with collecting the tribute paid to the temple service" (Lightfoot, "Galatians", London, 1896, p. 93, via New Advent)
The other meaning is specifically one of those called by Jesus for the special purpose of the Apostolate.
The Oxford Dictionary gives a generic meaning of disciple as:
A follower or pupil of a teacher, leader, or philosopher.
The specific meaning is given as
A personal follower of Christ during his life, especially one of the twelve Apostles.
A definition of apostle is
An important early Christian teacher or pioneering missionary.
Apostle is from the same Greek word as post and conveys the sense of a messenger of Christ.
Prior to the Ascension Peter etc. were essentially following Jesus and learning from Him. They were disciples. After Whitsun they were teaching about Him. They were His apostles. So the fundamental difference is between learning and teaching.
They also conducted a preaching tour during Jesus' earthly ministry. So at that point they were both.
In practice, though, people often use the terms interchangeably.
From the word root, "apostle" means "one who is sent" (similar to the English word "post"). Jesus sent his 12 disciples/apostles out in Matthew 10:5, Luke 9:2, and Mark 6:7. He also sent out 72 disciples/apostles in Luke 10:1. In addition, we have the Apostle Paul who was also sent (after Jesus' resurrection and ascension) by Jesus to the Gentiles (Eph 3:9).
In contrast, "disciple" is a student (one who disciplines themselves to learn).
Both words could apply to any Christians, since Christians today are taught to obey everything Christ taught the original disciples (Matt 28:20), including being a student and being sent. However, "apostles" usually (i.e., in most denominations) is used in reference to those who were directly sent by Christ.