Ok, this should give you a little clarity on your questions.
Each download is a seperate product, installed in different methods.
The ESXi Installable download is the hypervisor itself. This will generate an ISO to boot your host from and to install the base ESXi image.
After installing the host(s) you will want to deploy the vCenter Server. This is the management software. While it's not "Needed", there is considerable additional functionality that it will bring, especially if utilising more than one host. Automation and management (as well as deployment of virtual appliances *does* require vCenter server, so I would recommend installing even if you only have the one host - if cost is an issue install the appliance. Depending on your use case, you may find that deploying the Appliance would suit you better and potentially save you a windows license (otherwise you will need to create a windows server and then install the vCenter Server software onto it. This can be installed on a physical or virtual machine). One of the limitations currently of deploying the Appliance rather than the version installed ontop of an operating system is that the Update Manager software would need to be installed on another machine, where it's common to install the vCenter Server and Update Manager software on the same machine (update manager is a compoment of the vCenter Server installation)
With the latest release, VMware have started to include the Operations Manager Foundation software. Operations Manager installs as a virtual machine appliance and is used to monitor the health of the environment. While this isn't required, I would highly recommend it. There are more comprehensive versions available should you want to do more. A comparison of the versions can be found http://www.vmware.com/products/datacenter-virtualization/vcenter-operations-management/compare-editions.html
I would recommend that you download and read the installation documentation from https://www.vmware.com/support/pubs/vsphere-esxi-vcenter-server-pubs.html
Hope that helps... If you need any further information then please write back. If this email provides the answers you were looking for, please mark my response as answering your question.
Regards,
Jonathan