When you record in 480i/24p you can record in DV, DVCPRO, or DVCPRO50.
When the digital video standards first came out, different manufacturers implemented the standards with slight differences.
The quality of recording in the DVCPRO family of codecs runs DVCPRO25 (which is also called DVCPRO), DVCPRO50, and then DVCPRO100 (which is also called DVCPROHD). These formats were devised by Panasonic. DV is really the same quality as DVCPRO25, but was invented by another manufacturer, and it became the standard for miniDV tape.
So normally, for the most compatibility you would choose DV mode unless you were working with other cameras that record in DVCPRO. And then you'd want to record in DVCPRO so that all the files were in the same format when you got them in post.
DVCPRO50 provides 720x480 resolution, but it records in 4:2:2 color instead of 4:1:1 color -- so it has double the color resolution. That extra color headroom is great for color correction and critical for doing green screen chromakey work. Of course it produces files that are about twice the size of DV. And because it is storing twice as much information you can't save it to DV tape, only record to P2.
When you are recording in HD mode, the HVX200 camera records in DVCPROHD, which is different from the HD recorded by other manufacturers that have standardized on HDV. HDV records a "true" 1280x720 image, but drops the color to 4:1:1 and uses a compression method that grabs blocks of frames at a time. All this compression enables HDV to be recorded onto miniDV tape. DVCPROHD records in the 4:2:2 color space but with anamorphic pixels -- 960x720 which has to be stretched out to 1280x720 in post. So with DVCPROHD you get less horizontal resolution than HDV but more color. The HVX200 only records in DVCPRO, DVCPRO50, and DVCPROHD and does not record in HDV.