The Wikipedia article is using modular addition as it's more accessible to the layperson than a binary XOR, but they're functionally equivalent for the purposes of cryptanalysis. XOR is just modulo arithmetic on single bits instead of larger numbers.

Edit for your edit: All of this discussion applies the same for additive OTP as it does for XOR OTP; once you have depths you can start applying the OTP (however it's done) “in reverse” as it were to begin extracting patterns in the data.