So I fired up fh4 to see what it does and yes it just adds a delay before it auto clutches and changes gear. You should have noticed the rpm jump up and also in cockpit view there's some scratching sound. I guess that's their idea of what grinding sounds like but it's not a realistic sound like most sounds in game. I do prefer a stick when driving a real car vs paddles but a shifter is an extra and most of the real supercars have paddle shifters. I don't enable clutch in game because paddle shifter cars don't have a clutch pedal unless it's a sequential. Having a clutch would help with drifting to be able to clutch kick but it's easy enough without it.
Shifter type is functionally the same other than pushing a paddle vs moving through an h pattern (which can also skip gears while paddle is sequential). With manual+clutch: let go of gas, press clutch, paddle or stick shift, let go of clutch, press the gas. With just manual without the clutch setting, I can just push the paddle (stick should be the same) and you also don't need to let go of the gas.
I honestly don't use the wheel in fh4. Some cars are completely uncontrollable and auto countersteer can't be completely disabled which makes cars snap oversteer even when not using a wheel. Fh3 was better for wheels. These games were never marketed as sim games and are typically labeled as simcade since you do need to at least brake on some turns. You can easily tell how fake it is from the braking distances. They're a fraction of how long they should be. If you want a sim racing game try project cars 2 or assetto corsa competizione. If you haven't played a sim racing game and couldn't tell fh4 was simcade, I'd have to warn you sim racers are not for everyone.