Actually they do not weigh the same. The 9g and 7.8g are the weights in grams
Info came from
http://www.servocity.com/html/futaba_servos.html
S3107 weighs 9 grams, 0.3 ounces. Operates on 4.8 volts only. Has bronze bushings for the shaft
S3114 weighs 7.8 grams, 0.27 ounces. Operates on 4.8 or 6.0 volts. Plastic case serves as bearing
The difference is only 0.03 ounces but that matters in some applications.
The bronze bushing in the 3107 costs more than a plain case, and adds weight, but probably makes the servo last longer before wear makes the shaft wobbly.