Location high accuracy mode with wi-fi turned off
No, high accuracy mode without WiFi is not the same as device only because 


The mobile network provider location source is also used in high accuracy mode but not device only. 
Assisted GPS may be used to reduce the time to get a location fix when you use a network connection, either WiFi or the mobile data connection. "Download GPS assisted data only over WiFi networks" determines whether the mobile data connection is used for assisted GPS. Information about the GPS satellites expected to be in view is passed over the data connection, and this is much faster than the GPS receiver searching for satellites. 


No, for high accuracy mode "to actually work" does not require WiFi. GPS provides better location accuracy (~5m) than WiFi location (~25m) regardless of whether WiFi is enabled. That is why it is called high accuracy. WiFi location is much faster than GPS, but not as accurate. For many applications, it may be sufficient to know what city you are in but not what street.