What's the difference between "distributors" and "resellers"?

The two words are often equivalent, but distributor often implies a closer relationship with the manufacturer (as does dealership). The organisation may even be a wholly- or partly-owned subsidiary of the manufacturer.

A reseller often has a looser relationship with the supplier. They may not carry full stocks of spare parts, for example, and their staff may be less knowledgeable about the products.

This distinction can be seen by implication in OP's example, where the "channel partners" are listed in sequence from most- to least-closely associated with the supplier VMware.

To my understanding, it has to do with the chain of distribution from the manufacturer to the end-user or customer.

A distributor does imply a closer relationship with the manufacturer. Essentially, a distributer buys direct from a manufacturer and sells to either resellers or, sometimes, the end-user directly.

A reseller usually buys from a distributor or a wholesaler to get the best deal and sells directly to the end-user.