1. What's the difference and which should I be using for the Pi Zero W?
Eclipse Paho - Eclipse Mosquitto
2. MQTT is an app/program run on pi or or programming/unix type protocol?
MQTT is the name of the protocol - mosquitto is the name of a program that will run an MQTT broker (what would could be termed the server part of the deal)
paho is name used my some of the client libraries - the code you use to send and receive msgs from a broker - I use the Paho Python libs in all my programs but there are other libraries for other languages)
I don't want to have this on the internet, so no webserver.io address. Just my own little intranet if you will. So I need to establish an Access Point and Webserver on the Pi. Then running mqtt, create Clients, Publishers, URI/URLs? Am I getting it or even close?
I run mosquitto on my main windows PC (as its on all of the time) and all my little Pi around (and outside) the house send and receive msgs to/from it
I could just as easily run the mosquitto broker on any of my Pi but I just decided to stick with using my main computer - any computer would do the job for you
There is no need to run a webserver unless you need to.
If you do decide that you need a webserver to use to send/recieve msgs - then things get quite a bit more complicated and I'd recommend just starting off simply using a bit of Python code - let us know when you are ready to start and we can post some basic examples for you
So I haven't got the need to use a Pi as an access point as I already have a WiFi router in the house - but it should be possible to set up a Pi to do everything - be a WiFi access point and run a mosquitti broker at same time - I just have no experience of doing that