The development board has additional circuitry in it, including a serial adapter so it can talk to your computer over USB. It's an appropriate choice if you plan to use it as a standalone microcontroller. It's less appropriate if you want to use it as a wifi adapter for another microcontroller.
NodeMCU is used in reference to both the software, and development boards that are clones of the original NodeMCU board (the one you show a picture of is one of the countless NodeMCU clones)
The ESP32 is a much more capable microcontroller, but also more expensive (like $5-7 instead of $2), appropriate for use as a standalone microcontroller - it's not the sort of thing you'd use as a wifi adapter.