Sometimes the version you ask Claude Code to install is the version that is already running, for example during a reinstall. In that case it now copies its own running program file into place instead of downloading it again. This only happens when the download's signature has been verified and an extra safety check passes.
After copying, Claude Code compares the copy's checksum with the expected one. A checksum is a fingerprint of the file's contents. If the copy fails or the checksum does not match, Claude Code downloads the program as before. It reports either "Copied the running program as" or "Could not copy the running program, so downloading it".
Installing or reinstalling the version you already have no longer needs a download, and the copy is still checked against the expected checksum.