I’m not quite sure what difference you’re referring to with " there is a difference between that and the output of Inspect and View on IPFS Gateway" but the differences that I’m seeing from what you’ve posted is. the first url is a CIDv0 and the second one is a CIDv1. I can’t tell if they refer to the same content but I’m guessing that they do.
The third url is is rewritten to include the CID as a subdomain to avoid same origin problems and was introduced in IPFS 0.5.0 but was also rewritten to access it through your local node on the standard getaway port 8080.