If you couldn’t tell from my previous answers to these kinds of questions, I highly recommend the Etymological Dictionary of Biblical Hebrew, which is based on the works of Rav Hirsch.
The entry for פנה, pages 202-203, interprets the root as “turn to and focus attention.” Usage #8 is the one relevant here: “corner; walls joined from different directions” (emphasis mine). In other words: the word פינה, when used in the sense of a corner, refers to an interior corner.
The entry for כנף, page 120, interprets the root as “cover and conceal from view.” Usage #4 is the one relevant here: “corner; edge” (emphasis still mine). Seemingly, the distinction between כנף and פינה is the difference between the corner of a room versus the corner of a garment or a wing (I actually don’t see this usage in any other sense).
The entry for קרן, page 233, interprets the root as “project upwards.” Usage #4 is the one relevant here: “corner elevations” (emphasis still-okay, you get the point). Here the distinction seems to be not just any type of corner, but one that goes upwards, unlike the interior corner of a room or the flat corner on an edge.