The same meaning for both? Not so, the true pedant says.
Enquiry: Your neighbor tells you he is taking a two-weeks vacation abroad and will visit ten or two famous cities. Your jovial enquiry is: “Do you really expect to see anything on that schedule, or will you just bring back traffic reports?”
Inquiry: This can be a searching and exhaustive action – an official investigation of a crime, one that does not end until some murderous or brutal tragedy has been solved.