adb reboot vs adb shell reboot

No difference. Ultimately both set sys.powerctl property to reboot,<reason> ^{(1, 2)}. init then handles the property to proceed a proper shutdown or reboot ⁽³⁾. reason string optionally describes why the device was rebooted (see persist.sys.boot.reason property after reboot).

When executing adb shell reboot you make adb run shell: /system/bin/sh which then executes /system/bin/reboot binary. You can also set the system property manually:

~$ adb shell setprop reboot,just_testing