Frame rates? Progressive/interlaced

Well, 50i and 25i are usually the same thing. The "i" stands for interlaced and 50i means 50 FIELDS per second interlaced and 25i is 25 FRAMES per second interlaced.

Each frame is made up of two fields, this is the technical details for HD video:
http://www.itu.int/dms_pubrec/itu-r/rec/bt/R-REC-BT.709-5-200204-I!!PDF-E.p...

The first field scans the picture as a series of lines and the second field then scans a set of lines in between the lines making up the first field, and those lines are numbered in the order in which they are scanned, so the first field of a frame is called field one and has lines numbered 1, 2, 3, etc, and the second field is called field two and contains lines numbered 563, 564, 565, etc, and line 564 goes in between lines 1 and 2 (and so on).

[People do use other ways of describing the fields, but I think you can't go too far wrong if you use the official published definitions as above.]

They both exist - it's just two different ways of describing the same thing.

An interlaced video frame is processed as 2 fields. Those 2 fields are interlaced to form a frame. So, 50i is 50 fields that make up 25 frames. 25i would tell you that there are 25 interlaced frames per second.

Progressive frames have no interlacing. The entire frame is processed at once.