Simplex simply means that a channel is one-way or unidirectional. So a given channel will only ever send data from a device to some other device, or receive data from that other device to the first.
Dual-simplex is a pair of simplex (one-way) channels pointed in opposite directions, using one channel per direction.
Half-duplex is a communication system could be used to communicate in either direction as long as that communication doesn't occur at the same time. In other words, if it is acting in TX mode, one must wait until it finishes transmitting whatever it is transmitting, only then can it be switched to RX mode. Walkie-talkies or other push-to-talk systems are a good familiar example of half-duplex systems.
Full-duplex is a communication system that can be used to communicate in either direction at the same time. A good, familiar example of this the phone. You can talk at the same time and hear each other, even talking over each other.
The difference here is subtle. It is important to understand that half- and full-duplex refer to communication systems, whereas simplex and dual-simplex refer to single channels.
A single channel can be full-duplex only if one can communicate in both directions at the same time on that channel. If one takes a dual-simplex pair, that pair as a system is full-duplex. But full-duplex does not imply any sort of mechanism or architecture, it only means that communication can occur in both directions simultaneously.
Dual-simplex is referring to a specific way of using 2 simplex channels: one tx and one rx. This is a means of achieving full-duplex communication, but dual-simplex could also implement half-duplix communication if some other limitation prevented the rx and tx wires from both being used at the same time.
Put simply, duplex can applied to any level of abstraction and only cares about how communication at that level can behave. One would say that the PCIe bus is full-duplex.
Simplex describes single channels at the same level of abstraction of said channels, specifying the topology of a single channel (or a pair of them in dual-simplex's case). One would call a single PCIe lane dual-simplex. You can also call it full-duplex as well but that is not quite as specific - it could be any number of channels, and each one might itself be half duplex or some other odd arrangement.