On this model Fuji's extended DR function doesn't really alter the dynamic range of the sensor (if there were a way to increase DR it would be on all the time).

Instead it gives you more room to recover highlights (which to most people makes it seem like dynamic range has increased) which is done by underexposing the shot. The reason for the increased minimum ISO when using, say DR400%, is that this mode uses the same amplification as ISO200 (it's not possible to underexposure a base ISO shot without changing shutter speed or aperture). This produces a signal underexposed by two stops, which is corrected in software. The advantage to correcting in software is that you can detect when highlights would be clipped and prevent this from happening.

So to answer your question, there is indeed a difference between shooting at ISO800 and shooting with DR400% and ISO800 - the former uses hardware amplification only, the latter uses software amplification only (DR200% uses half hardware, half software). Using software amplification carries with it increased shadow noise. This is because amplification happens post readout so you amplify the read noise, which doesn't happen if you amplify before readout.

If your sensor has very low read noise anyway then the increase in noise when using this approach can be pretty small. But there is still some noise penalty which is why (in addition to the inability to use wider apertures/longer shutter speeds) this setting isn't always on.