Independent creation only applies to copyright. If I independently write the same code as you, we both have copyright on it.

Patents exclude independent invention. If we both invent the same thing and I have the patent, you cannot use your invention.

Trademarks allow independent creation in separate geographic areas, but a pre-existing use can exclude an independent creation.

This is one of the many reasons that "Intellectual Property" is a misnomer - the differences between copyrights and patents and trademarks are probably larger than the similarities.