What's the difference between VMware vCenter and vSphere?

I've seen several inadequate answers to these questions recently, including those from VMware. This post is to offer clarification. 

What's the difference between VMware vCenter and vSphere?

vSphere references the suite of products, an umbrella term, of offerings by VMware of which vCenter is the centralized solution to manage many of the VMware solutions. vCenter is not vSphere, but vCenter is a component of the vSphere umbrella of vSphere products. 

What is vSphere?

vSphere is not a single sofware installation... it is a suite of products that work together to provide virtual machine and networking solutions. At a minimum, the vSphere exists when VMware vCenter and VMware ESXi are used together.

What is vCenter?

vCenter is server software that manages physical ESXi server. vCenter provides the centralized management and function vSphere offerings. At a minimum, vCenter manages ESXi servers and delivers features like vMotion, ESXi Clustering, UpdateManager, vRealize Operations Manager, NSX (Virtual Networking), and so on. VMware offers many solutions that are centrally managed within the vCenter.

vCenter is a software package on a Windows server OR a dedicated virtual appliance  running on VMware's home grown OS (called PhotonOS).

What is ESXi?

VMware ESXi is the Hypervisor which installs directly onto a physical server. ESXi abstracts the hardware and runs virtual machines. While ESXi installs directly onto computer server hardware, it is not an operating system but an abstraction layer between the Operating Systems (Windows, Linux, x86 OS architecture) and the hardware. This abstraction layer allows the Virtual Machine features & capabilities which would not otherwise exist, such as: 

• Portability  (the ability to move the operating system to different hardware platform (like moving from Dell to HP) with minimal or zero downtime. 
  
• Eliminates hardware vendor locking. 
• The Hypervisor enables multiple, different Operating Systems to run concurrently at the same time.
• Allocation of resources appropriate to the application Operating System.
• Isolation: The same hypervisor enables isolation applications and operating systems from one another even though they concurrently execute on the same computer hardware.

What is a virtual machine?

A virtual machine is a presentation of physical hardware appearing to an operating system (OS) to standardized set of hardware. To an installed OS like Windows or Linux, the virtual machine looks like a REAL MACHINE. In practice, and OS doesn't "know" it is running as a virtual machine or real machine.