Storage.googleapis.com or storage.cloud.google.com for signed URL

I sign the GET url to GAE and pass it to my client app so that it can download the file from google repository directly. If the client application sends a request for the storage.googleapis.com file, it receives a SignatureDoesNotMatch response. It works if the request is sent to storage.cloud.google.com (still gets 302, but I think it will work if redirected).

But if I create a signed url in my local app (not in GAE) then the request works (the file is loaded) using storage.googleapis.com.

I would like to know what is the correct url to send a signed url request and why the difference in behavior is between the GAE signed url and the url signed local app.

Getting started with PUT requests, the URL signed generated from the GAE request for the PUT request does not work (403, 405) with any domains, although the local URL signed app does. I am confused by this strange behavior.