Why both no-cache and no-store should be used in HTTP response?

I must clarify that no-cache does not mean do not cache. In fact, it means "revalidate with server" before using any cached response you may have, on every request.

must-revalidate, on the other hand, only needs to revalidate when the resource is considered stale.

If the server says that the resource is still valid then the cache can respond with its representation, thus alleviating the need for the server to resend the entire resource.

no-store is effectively the full do not cache directive and is intended to prevent storage of the representation in any form of cache whatsoever.

I say whatsoever, but note this in the RFC 2616 HTTP spec:

History buffers MAY store such responses as part of their normal operation

But this is omitted from the newer RFC 7234 HTTP spec in potentially an attempt to make no-store stronger, see:

https://www.rfc-editor.org/rfc/rfc7234#section-5.2.1.5

Under certain circumstances, IE6 will still cache files even when Cache-Control: no-cache is in the response headers.

The W3C states of no-cache:

If the no-cache directive does not specify a field-name, then a cache MUST NOT use the response to satisfy a subsequent request without successful revalidation with the origin server.

In my application, if you visited a page with the no-cache header, then logged out and then hit back in your browser, IE6 would still grab the page from the cache (without a new/validating request to the server). Adding in the no-store header stopped it doing so. But if you take the W3C at their word, there's actually no way to control this behavior:

History buffers MAY store such responses as part of their normal operation.

General differences between browser history and the normal HTTP caching are described in a specific sub-section of the spec.