Replay mode it seems from the videos like P3D/FSX/X-Plane and I guess most other games that have this doesn't look as smooth as the real gameplay. It looks like the aircraft is on rails sometimes and not moving through the air.

I've seen a lot comments about the smoothness of the videos or how the planes appear to handle etc. I think the above probably explains why you see that.

You can tell the video was shot in replay mode because they will be flying the aircraft in a way the autopilot might i.e smooth turns following a course but the autopilot panel lights are not switched on! 

nice idea but there isn't a replay mode, there is however a copilot feature, separate from the in aircraft autopilot

lmao...There is no replay mode in the game as of now.

I'm afraid the OP is mistaken, because there isn't a replay mode as of yet. Hopefully, one will be added soon. However, I've heard streamers say that it's difficult to stream/record MSFS without stutters, but according to them the sim is butter smooth even though you see stutters in the video. I am not a techie, but my assumption is that the sim utilizes your hardware in such a manner that it can produce a smooth experience for your sim, but it doesnt have much leeway when it comes to additional programs running (ie. obs etc).