The commonality of serial with the lifting body behind is explained in my upload of the latter here - the X-24A underwent radical changes when rebuilt as the X-24B which flew 36 times between 1973 and 1975, making 12 gliding-only and 24 powered flights with gliding landings as part of the Space Shuttle development program. Each time, a NASA modified B-52 mothership launched the X-24B at 45,000 ft. It was moved to the USAFM in 1976

This was originally the jet-powered Martin SV-5J, a derivative of the X-24A lifting body built for flight training but never flown. For display purposes, the SV-5J has been modified to represent the X-24A. Martin donated it to the museum in 1971. In 1973 the actual X-24A 66-13551, which made 12 gliding tests in 1969 and 1970 dropped from a NASA modified B-52, was converted into the radically different 'flat-iron' X-24B on display alongside

This is a jet-engined SV-5J that was converted to X-24A configuration for display purposes.