Came here to post this, but as a former Square employee I can tell you they designed the "puck" reader from scratch years ago and contracted directly with the manufacturers. Stripe clearly copied the industrial design but I'd imagine the internals are different. It will be interesting to see how Stripe fares with this - in person payments are a very different ball game than online. PayPal and Amazon have tried with what seems to be limited success.
I too am ex-Square, and in fact I worked on the firmware for the [https://squareup.com/us/en/hardware/contactless-chip-reader]... Reader for Contactless and Chip). All hardware design, from the external design through the mechanical and electrical is done in house.
Not going to say that Stripe was uh... influenced by the design, but I do think that imitation is a nice form of flattery.
Square designs all their own stuff. It looks similar because Square did a good job on their chip reader and because there are only so many ways you can make a chip reader without a keypad.