Should I purchase my PS4 games from the PS Store for PS Vita Remote Play?

Hello.

I have got myself a PS4 and so far I'm loving it even though I currently only have Killzone Shadow Fall. I have been looking around online and have also been thinking about buying a PS Vita so I can stream my PS4 games to my PS Vita when I want to leave the living room or when the TV is occupied. When I was looking around online for reviews I noticed the reviewer was able to switch game to game without touching his PS4, does this mean he purchased all his games through the PS Store or is it one I have installed a game on my console I can load any of them without inserting the disc?

I ask because if I am going to get a Vita it would be so much better if I didn't have to keep switching around disc every time I wanted to load a new game remotely.

Thanks in advance, Matt