All videos and photos are recorded to the sd card in the camera and not the st16.however the videos and photos are also captured in the st16 internal memory at lower quality for preview purposes.
I believe the camera will take cards upto 128gb but I have a 64gb one in mine and I find its plenty big enough,the trick here is to buy one with as high transfer rate as possible especially as the H records in 4K,this will be written on the sd card packaging as transfer/download rate,somewhere up in the 90's is ideal and will be fast.
There is no need to have a card in the st16 but if you are going to replace the card in the camera you may aswell pop that one in the st16 for transfer of telemetry files if necessary,myself and a few others have found,16/32gb cards work best in the st16,I've tried my 64 in there and it will not mount.