The round-pin is the 75-ohm coaxial PAL connector. This is for use if you need to bring in weaker signals using an externally-mounted antenna on your roof, or on a pole. The coaxial shield is grounded, and this helps prevent interference from Airconditioners, fluorescents, etc.
The 2 rectangular pins (300-600ohm) are a proprietary B&O connector, for an internal FM antenna (Bunny-ears). Use this if you have lots of strong transmitters in your area, and you need to reduce the length of the antenna to prevent "bleeding" of one signal over another.
There is also a very similar B&O AM 2-pin connector. It has one of the pins rotated 90 degrees. At a casual glance, it appears that they are identical, but you cannot insert an FM connector into an AM socket, or vice versa.
The so-called 2-pin AM socket on YOUR BM4400, is probably a non-exact replacement from a previous repair! The BM4400 is absolutely FM only.
Menahem
Learn from the mistakes of others - you'll not live long enough to make them all yourself!