After a little web searching, I found this article on acronyms on Yellow-Bricks which reveals the little known/cared about story of many terms in VMware’s world of virtualization. There is also this link to a video interview with Mike DiPetrillo which goes more in to this matter.
ESX and GSX
As VMware old-timer Mike Di Petrillo tells us, the first hypervisor versions were named by a marketing firm as:
Elastic Sky
Ground Storm
The engineers did not seem to like it and after a vote from the engineers they dropped the long names and retained the initials and added the X to make it sound technical. Hence, the next versions of hypervisors were named:
ESX stands for Elastic Sky X
GSX stands for Ground Storm X
ESXi
Apparently, the “i” in ESXi stands for Integrated, probably coming from the fact that this version of ESX can be embedded in a small bit of flash memory on the server hardware. In this manner, we can treat server hardware almost like a hot-swap commodity; just another node.
VMware vSphere Hypervisor
To confuse things further, VMware now offers the free VMware vSphere Hypervisor (intended to replace the “free-ESXi”, and separate from ESX/ESXi, which are Enterprise-class hypervisors). For more info, see this FAQ from the VMware website for VMware vSphere Hypervisor.
What is the difference between VMware ESXi and VMware vSphere Hypervisor?
VMware vSphere Hypervisor is the new name for what was formerly known as VMware ESXi Single Server or free ESXi (often abbreviated to simply “VMware ESXi”). VMware vSphere Hypervisor is the free edition of the vSphere production line. It is licensed to only unlock the hypervisor functionality of vSphere, but it can be seamlessly upgraded to more advanced offerings of VMware vSphere. VMware vSphere is available in multiple editions, including several options specifically designed for small businesses.
VM.Blog. 
Nicely described for the novice to VMware technology what is what to enter into this technology.
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Elastic Sky would be a good name for a band. Esp. if the band members were computer nerds. No offense intended; I am a computer nerd… why else would I be on this page…
In other words, Elastic Sky was an attempt at advertising strategy “symmetry.” The symmetry is suppose to position the product in your mind so you remember it if you happen to be in the market for something like it. It isn’t that easy…even Britney Spears couldn’t sell Coca-Cola!