Accessing macOS Recovery Mode without Internet access?
The Recovery Partition on the system disk corresponds to the version of the macOS installed and should be loaded when holding CmdR at boot (not CmdS). However, if there is no recovery partition on the disk it will automatically revert to Internet Recovery which means downloading the boot image from Apple servers. Mac will also do that if there is a version mismatch from Recovery and macOS version installed. Remember that you should be able to use option key at boot which invokes Startup Manager which lets you select the available boot volumes, including the Recovery partition (without downloading from the Internet).

Nonetheless, according to HT204904 there are actually several key combinations for Recovery:

CommandR - Install the latest macOS that was installed on your Mac, without upgrading to a later version.

OptionCommandR - Upgrade to the latest macOS that is compatible with your Mac

ShiftOptionCommandR - Install the macOS that came with your Mac, or the version closest to it that is still available.