What's the difference in shooting 25F with 1/50 shutter speed and 50i with 1/50?
 

I'm using a pal A1 and when set to manual mode, I was wondering if there is a difference when you set the mode to 25F and shutter speed to 1/50 or the mode to 50i and shutter speed remain at 1/50 or vice versa.

Each picture frame in a PAL video stream consists of two interlaced fields, one containing odd lines (the horizontal lines you can see on an old CRT Tv-sets), the other the even lines. 50i mode (the normal TV mode) shoots a picture every 1/50:th of a second, so these fields are not exposed at the same moment, but 20 milliseconds apart. Each exposure is used for odd and even frames, resp. This gives the effective frame rate of 50 pictures/sec, but the vertical resolution is slightly compromized. This gives fairly fluid illusion of movement and is the way all tv-sets operate.

25F mode frame has also two interlaced fields, but they are exposed at the same moment. The first exposure is used for both fields and the second discarded. This gives a frame rate of 25 pictures/second, which makes movement much more jerky, but resembles movie film, where there is naturally no interlacing and the frame rate is (only) 24 fps. Resolution is slightly better, though.

In my opinion 25F should only be used for strobing effects or when the footage is going to be transfered to film (never happens to people who have to ask this kind of questions). 50i looks more natural and fluid.

Also, 1/50 is the correct/standard exposure for both 50i and 25F.

This is the standard exposure for 50i and matches the frequency of the electrical system. Faster shutter speeds are used for "sharper" action. Very fast shutter speeds are used when the footage will be slowed way down to prevent a series of blurs on play back.

For progressive shooting, the film standard is a 180 degree shutter, which translates in PAL land where 25F is shot to 1/50 a second. A 180 degree shutter amounts to 1/2 the frame rate. Again, a faster shutter speed can be used for special looks and effects.

In both 50i and 25F, there is one full frame every 1/25 of a second, just recorded differently as explained above.