This comment confused me so I looked up the definition of homophone[0].
Turns out it can mean two words sounding the same (definition 2) or merely sounding alike (definition 1). Personally I always thought homophones had to sound identical. But you are right, they are homophones in the broad sense.
Any difference quickly disappears once you take into account various accents and dialects. It's a lot like pin and pen. They're technically not by the strictest sense of the word homophones because there should be a slight difference in how you pronounce them, but in practice, there is no difference.