The Crux Simplex or Stipe, being a simple upright post, does not have the transverse beam found on other forms. The ancient Greek word for stake is stauros (n) and stauroo (v). This simple post was common for crucifixions until the Phoenicians added a cross beam.
The Crux Simplex evolved from a tree (an infelix lignum or an arbor infelix) dedicated to the gods of the nether world. Such trees are non-fruiting, unproductive, valueless, and therefore considered appropriate to use in crucifying criminals.
Historians and etymologists have debated whether the scaffold in early Scriptures meant Jesus was executed on a simple upright post, or a post with a cross beam (either a ✞ shaped Latin Cross, a 'Y' shaped Forked Cross, an 'X' shaped St. Andrew's Cross or a 'T' shaped Tau Cross). The common belief is that it was not a simple upright post, but the distinction is nowhere nearly as important as the reason why Jesus was executed.
The Bible says that Jesus was hung on a tree1. Whether it was an actual rooted tree or an upright wooden post set into the ground (see Broken Cross), the common consensus is that a transverse beam (patibulum) was then added. A usual crucifixion method was to bind the condemned person's wrists to a beam and then attach that beam to a tree or stipe, thereby forming a cross (crux composita or crux acuta).
The Greeks apparently used the word 'stauros' to represent a wide range of wooden structures used for executions, but Jehovah's Witnesses and a few others interpret the word to mean Jesus was executed on a post without a patibulum.
This is a moot point. The fact remains that Jesus was crucified and died that our sins might be forgiven. See Why Jesus Died.