Hi,
vSphere - Commercial name of VMware's server virtualization product
vSphere Hypervisor - Commercial name for the free version of ESXi
ESXi - Name of the hypervisor used and developed by VMware on all of its "vSphere" products
From the download page of your evaluation, you will download ESXi so after you first install ESXi, you do it in "eval mode". This is simply because the hypervisor itself is the same for both paid and free versions.
The thing that changes is the licenses features. So in order to obtain the "vSphere Hypervisor" features, you need a key. Otherwise, you will be running a fully functional trial. That key is in your "My VMware" or in the same page from where you downloaded your binaries.
So, go to the host>Configuration>Licensed Features and add your vSphere Hypervisor license key.
Then, you will see something like:
Product: VMware vSphere 5 Hypervisor Licensed for 2 physical CPUs (unlimited cores per CPU)
License Key: xxxx-xxxx-xxxx-xxxx-xxxx
Expires: Never
Product Features:
Up to 32 GB of memory
Up to 8-way virtual SMP
As you can see it never expires and I promise you I didn't pay a dime for this :smileyhappy: So, yes, "vSphere Hypervisor" is completly free as advised.
I also tried to explain the differences between the namesof the products just in case there was some confusion with them, if there wasn't, sorry for giving a "heavy reading" answer.
Hope everything is clear now!!! Good luck!
Regards,
elgreco81