There is no "BW filter". There's "B+W" which is a BRAND NAME for high-end filters.
So the difference is... When shooting in BW mode straight from camera, you will get a black and white picture. When using a B+W filter, you will get the effect of the filter (polarizing, ND, GND, etc) unless it's a UV filter in which case you get no effect.
When shooting Black / White straight from cam the image conversion is done in the cam according the limited options cameras offer. Once it's Black and White there's no way back and your post-processing options are limited as well.
Better shoot RAW and use the software that came with your camera.
shooting b&w starlight from camera, if you want a color version of the images later on is pretty a gone case.
doing conversion at the post you will have more control and than using convention b/w contrast filters.
and the b/w contrast filter is original design to use of b&w film, you need to understand what subjects you are dealing with before you decide which filter to use, there is not really a filter can fit for all type of situations.
if I'm intending a day's images to be eventually converted into black and white I'll use a selection of various color filters to enhance certain zones within the grayscale
but be mindful that the 'color' output is going to be sporting a color cast unprocessed