In both cases you're using a private key, which you need to protect, to authenticate you are who you say you are. I suppose the difference is a JS bundle could be signed offline and uploaded to a potentially insecure server/CDN/app store/whatever.

The fact that a private key is used doesn't mean HTTPS and code signing are the same.

HTTPS says, "The communications you send to the server cannot be intercepted and changed between the client and server, and the identity of the server you're connecting to has been verified by one of your trusted certificate authorities."

HTTPS promises that your communications cannot be snooped on, and the person you're talking to is verified by a mutually agreed upon third-party.

Code signing does something entirely different. Code signing says, "The code you're about to run was written by the developer specified in the signing certificate, and has not been modified since it was signed. The identity of the developer has been verified by one of your trusted certificate authorities."

So the practical difference is this:

Say your browser requests https://domain.com/random.js. HTTP ensures that you're connecting to domain.com, and that your communications won't be changed or observed in transit. However, it does not guarantee that some malicious third-party didn't overwrite random.js on the server. With code signing, you can accomplish that. An author can "sign" a code package so that any alterations to the code itself would cause a certificate invalidation.