Don't know which is which, but I would say one of them has a higher ISO setting than the other. A lower ISO setting should give you smoother, less grainy results. Could be the "intelligent" setting is giving a higher ISO. Only guessing as I don't even know what camera you're using, but grainy shots are often caused by higher ISO's.
I don;t know how NEX cameras work, but there are 3 variables to control how much light you allow to hit the sensor. Whether you control them or the camera does is up to you. But once you get a basic understanding of them, it'll help you take better photos. the 3 variables are........
1. ISO (this used to be film speed....not sure what it really mean now. All you need to know is that the higher the number, the more light will hit the sensor (and the noisier or grainier the photo will be)).
2. shutter speed (this is how long the shutter stays open to allow light in). This is usually fractions of a second.
3. the aperture or f-stop - the "smaller" the number, the more light gets in.
there are several different combinations of these to get a "correct" exposure. Since you shooting a stationary subject here you can use a longer exposure to let in more light (and the camera will choose or you will set a lower ISO) and it will be smoother.
Iam, you would want to use the lowest ISO you can......in full sun, use the very lowest ISO period (not sure on our NEX.....it's probably 100). Indoors, you may have to go up to 400 or 800 and the NEX does fine there.....in lower light you may need 1600 or 3200 and it should be pretty fine there, too.....you may even get away with using 6400, but you'll start seeing noise...especially when viewing large on screen, but in standard size prints, you won;t likely see much noise at or below 3200 on your NEX.
For example in your second shot, the ISO is 640 and the shot is nice and smooth.....the exposure was for 1/60 of a second which is quick enough that people can hold steady and you won't get blur, but if there's action that you want to freeze......say 2 kids playing, they'll just be a blur at that speed. So the exposure will have to be shorter, but to compensate, the ISO will need to be higher to be properly exposed. I really struggled understanding it all at first, but keep experimenting and it all sinks in eventually.
^ ...and make the heads in front of you more distracting in your final photo. You're better off using a higher ISO, but still the lowest you can get away with, which will depend on how quick a shutter speed you need to get the performer(s) sharp.
I generally think natural lighting is best. Flashes usually create distracting shadows. I think you'd be fine setting the ISO at 3200 and going without flash. Hopefully that will allow you shutter speeds that will be quick enough to freeze the action.