It is similar to the hang on filter, but just a bigger loop. Your hang on filter had the pump inside and it drew water from the tank and it overflow back into the tank. The sump is like the hang on filter box, just bigger.
We typically don't use as much direct mechanical filtration (filter floss or cartridges) in a reef aquarium. The live rock acts as a biological filter and the skimmer a mechanical filter. The filter sock in your sump is also a mechanical filter, but you may not want to run it all the time (it has to be cleaned every few days) but instead run it as needed (for example when using a small powerhead to blow detritus off of your rock).
There are no "rules" on how this all needs to be setup and maintained, but there are some well established methods. You will build it piece by piece and learn as you go, some if it trial and error.
We can tackle fish, coral (if that is your plan) and other livestock once you get the water circulating.
I would befriend your local fish store. It is good to have a relationship with the understanding that they usually mean very well, but don't always give the best (or even good) advice or carry the best (or even good) products. There are certainly many exceptions and some amazing local stores out there.