An SMS would have to relay through your phone, due to it having the phone service, so would show on both devices. It sounds like you had multiple iMessage identities (email1/email2/phone/etc.) and one of those was only enabled on the iPad.

I do not, and have never owned, an iPhone. I only have an iPad and a work mac and without trying it managed to make me lose a text. I managed to disable it and deregister my number but the deregistration process was extremely buggy and a pain to begin with.

Interesting. I don't understand the source of the SMS you lost, then. As far as I know, it's not possible to forward SMS from an Android or feature phone to an iPad or a Mac without some clever workarounds.