Hi Peter, and welcome to the Forums! You'll love Android, I'm sure, and the Note 4 will be a great phone to start!
Factory Unlocked means that the phone is ready to be used with any SIM card from any compatible carrier (if the phone supports the frequencies the carrier uses, you should be good to go as long as the carrier allows unlocked devices; some carriers in a handful of countries don't). If your phone is carrier-locked, it means it will only work with SIM cards from that carrier. These phones, however, can be unlocked by the carrier or by 3rd party (and less legal) methods.
Region Unlocked is not really a term that was common until Samsung made it popular with their newer phones. Basically, to thwart gray imports a bit, they region locked their phones, EVEN if factory unlocked. But what this does is basically require the phone to be used for the first time with a SIM card from the region the unit was supposed to be sold at. For instance, if the phone was meant for LatAm, the first call coming out of this unit should be done with a SIM card from Mexico or Argentina or any Latin American country. After this, and if the device was factory unlocked, the region restriction is off and you can now take it abroad.
Like the above post mentions, it is theoretically possible to have a factory (or SIM) unlocked phone with a region lock in place, but this wouldn't be too great for roaming and I have yet to find one that is. But then again, I haven't tried every phone out there, so the possibility is there. For these mainstream phones, however, I doubt it.