Industry standard ways of connecting boards / modules?
For board to board digital connection within the same enclosure, whenever possible I use ribbon cable with IDC connectors. That is fairly standard. For higher currents, I'd use a molex MTA connector with crimp connectors. I don't believe I've ever had to move a low-level analog signal between boards, so no idea what I'd do there. Shielded cable, but I don't know what connector I would use. Perhaps a mini SMA; I have an instrument that uses an LVDT and the connector to the LVDT signal conditioner uses SMA connectors. Ribbon cable is pretty standard for digital signals and can be purchased premade off the shelf.

Going outside the enclosure, well, things get complicated. My preference is always some form of circular connector because it's easier to drill/punch a couple of round holes than mill a rectangle. What I choose really depends on how many signals are needed.