The 77317-804-12LF: The 0.230" (5.84mm) mating pin length gives enough reach to engage a standard receptacle body; the 0.120" (3.05mm) solder tail fits through a 0.040" plated-through hole without bottoming out on the opposite side.
15µin Gold vs 30µin — A Plating Choice
The thicker plating buys roughly double the rated mating cycles in a corrosive or high-cycle environment. If the application sees frequent unmate/mate cycles or sits in a humid cabinet, the 30µin variant is the safer call. For a one-time board-to-board stack inside a sealed enclosure, the 15µin is adequate and costs less.