* Playfair's Axiom: This is the most common alternative name, attributed to John Playfair. It states that "Through a given point not on a given line, there is exactly one line parallel to the given line."
* Euclid's Fifth Postulate: This is the original name given by Euclid in his book "Elements," where it was stated as: "If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, will intersect on that side."
* The Parallel Postulate: This is a more general term that encompasses any statement equivalent to Euclid's Fifth Postulate.
In essence, all these names refer to the same fundamental concept in Euclidean geometry, which is the uniqueness of parallel lines.