My Lumix GH4 can film 4k in 25p , 30p and cinema 24p.
I was wondering , does 24p just mean one frame per second less then 25p, or is there a good reason why one should use it for filming anything to make it look cinematic?
It's more about delivery than "cinematic" look. If you're in PAL lands, 25fps will match with broadcast frame rate. If you're in NTSC lands, 30fps will convert most easily to broadcast standards. 24fps for a specific "look", to use higher frame rates for slomo, or for cinema package delivery. If you're not delivering for broadcast or DVD/BD, it's your preference - although not many in NTSC territories shoot 25 fps.
Thanks, I am in a pal region so 25p would be 'normal' for me.
I'm not sure what you mean by 'cinema package delivery', does that mean if you actually want to make a movie that is meant for actual cinema playback?
And higher framerates for slomo, does that have to do with the fact that you can use 24/30=0,8 factor to slomo your 30p footage into 24p, but would need a more difficult factor of 0,833333333 if you use 25p for the project?
"I'm not sure what you mean by 'cinema package delivery', does that mean if you actually want to make a movie that is meant for actual cinema playback?"
Yes, Digital Cinema Package is a set of specs for digital projection and the primary standard is 24p (a few higher frame rates are allowed)
For your second question, it's a matter of 24fps being seen as the standard "minimum" frame rate for smooth viewing and so you have the ability to use higher sync camera frame rates (as opposed to overcrank settings in some cameras where you can shoot 60 fps and have the header flag it as 24 or 30 for playback).
For years it's been typical to simply alter the speed of PAL by -1 fps (along with the audio) to move to cinema projection, or to alter film footage by +1 fps for PAL broadcast. If you want cleanest slo mo, disabling resampling is generally the way to go - and yes, then the math is important if you don't want dropped frames. If you can live with Vegas' resampling, then the math doesn't matter as much.
Edit: I should add that if you plan on maintaining PAL standards through delivery, a 25fps project would probably make your life MUCH easier than editing at 24fps. You've already worked out the math for slo mo use of your other camera speeds.