In total there are three ways to access remote play feature on Playstation 4 and PS VITA, “Direct Connection, Household/Local Connection and Out And About Wide Connection”
Check out the image below detailing all three ways to Remote Play between PS4 and PS VITA.
First Method Direct Connection:
It requires close proximity between both Playstation VITA and Playstation 4, very much similar to Wii U Style.
Second Method Household/Local Connection:
Connection to same local router required. Works if VITA is outside Playstation 4’s direct range.
Third Method Out And About/Wide Connection:
Connection to different routers. Works if away from Home, but in this case Lag issue will be the most.