Christian fundamentalists are Christians who follow the Five Fundamentals:
Inerrancy of the Scriptures
The virgin birth and the deity of Jesus (Isaiah 7:14)
The doctrine of substitutionary atonement by God’s grace and through human faith (Hebrews 9)
The bodily resurrection of Jesus (Matthew 28)
The authenticity of Christ’s miracles (or, alternatively, his pre-millennial second coming)
“Fundie” is more of a catch-all term, despite being derived from “Fundamentalist”. It usually includes a certain subset of evangelical Christians and pretty much any conservative Christian who lobbies for his or her religious beliefs to become law (or at least to become custom).
The term specifically refers to a movement in American Protestant community that started in the early Century 20th. The common use of the term “Fundie” while not 100% technically accurate is fairly close to the mark. The movement was specifically about the literal interpretation of bible and its applicability to non-spiritual matters.
The term was only ever used in reference to religions other than Christianity much later (Wikipedia claims during the Iran hostage crisis).