VMware is the company, vSphere is the overarching virtualization platform for cloud infrastructure. Think of vCenter as a central management console for virtual machines and networks. ESX and ESXi are hypervisors (the difference being how they sit on hardware). GSX is not really used anymore, see VMware Server.
I would suggest reviewing this page by VMware for the overall idea and go through their knowledge base for more finite explanations.
It is one thing to define each of the terms and another to see how they fit together.