Specifics change per heist, but I'll use three heists in the beta for example...
In the Bank heist (for simplicity, Cash version), the map is composed of a single bank building (with a roof you can access) and the streets around it. Firstly, across the map, the number and position of security cameras, security guards, civilians, and misc small safes is randomized, as well as the 'patrol route' of the guards. Where you start the heist from and where you end the heist at are also randomized between several possible positions across the map, and the position of certain important stage fixtures (in the bank heist, this is the main vault, the location of the security room, and the key card for the security room either being on the bank manager's person or laying in his office) have a few different possibilities of what they could be/where they are. Police Assaults when they're attacking is random as well as what they entail. Specifically on this map, when you open up the main vault, there is a chance that the money will be completely in the open with nothing blocking the way, or security bars will be in place you need to drill through as well. In this heist there also are a large number of deposit boxes, which have random contents inside (ranging from useless stuff like a book on rome and a sandwitch to some spare change, larger clunks of cash, or even gold).
Stuff like this change in a lot of campaigns, and there are stage specific things that can change, Another thing that can happen is in some certain heists that are multiple days long, you can randomly get an 'escape' or 'score' scenario, which is an extra stage where you either have to escape with your loot and not get caught, or have a chance to score higher and earn more money at a pitch-stop.
One thing to note is if you're trying to gauge the current mood of the stage, listen to the music. It's dynamic, will be slow and quiet when nothing is going on, slowly pick up and then accelerate and get intense when shits going down.