Your reference to IEEE Std 200-1975 is outdated by a couple of decades. This has been replaced by ANSI/ASME Y14.44-2008 (Reaffirmed 2014).
The Fig. 3 that has been shown above from IEEE 200 is Fig. 4 in Y14.44 and shows W2P1 and W3P1 as female/sockets with A7J2 and A9J2 as male/pins. This was done at my suggestion/insistence. No, P1 does not necessarily connect to J1, see the figure.
If two flexible cables connect with mating connectors each of the connectors is ref des with class letter P, thus a P can connect to a P but you would never find a J connecting to a J.
The question is how do you ref des mating connectors that have no gender/sex, like an APC-7 precision 50 Ω coaxial connector or connectors that have flat or D shaped “pins” that slide in against each other and are held tight by turning a lever? The answer is you treat each of them as a butt connector or male. The most fixed uses class letter J and the most movable uses class letter P.
Another question is how do you ref des a pair of mating connectors that have both male and female contacts (they do exist)? Again the most fixed uses class letter J and the most movable uses class letter P.
As for showing the contacts, whether they be male or female, in a connector the graphic symbol should not be drawn with a box or rectangle around them but should use mechanical connection lines (dashed lines) as shown in IEEE 315A, Clause 18.104.22.168, the 2nd (middle) symbol shown. Actually this comes from IEC 60617 and I would heartily endorse its use.