Both mean something that provides an additional benefit to the main item, but they are different like this: Attachment: must be physically "attached" or made part of the main item. A vacuum cleaner has attachments that hook to it. Accessory: could be attached or not.

As far as I can see, they are just synonyms used in the vernacular. The choice of word can simply be due to the established colloquial meaning. The speaker may choose to use the word "attachment" when talking in a mechanical context and the word "accessory" when discussing phones or fashion. In legal terms, you would use accessory (not attachment) when referring to an accomplice in a crime for instance. Context would dictate the appropriateness of these words (IMHO). I'm sure a hardcore grammarian will chime in if there is a grammatical connection..... :)

Accessory - usually something you can wear with clothes like Jewellery, belts and scarves. Something that helps make the look better or become more useful. You can also be an accessory to a crime by helping the criminal. Attachment - things that clip Or pin onto things. something that is attached to something else. An extension. You can also be attached to something or someone, which means you are fond of them/ like them. I hope this helps. Attachment and accessory can have very similar meanings.