I've noticed tension differences of as much as 16 pounds based on RacquetTune. So what you are telling me isn't that surprising.
I used to get my racquets strung by pro shops or by a friend. I would often ask for 56 pounds but my racquets would come in at the high 40's fresh from the stringer. I now string my own racquets with a drop weight machine with fixed clamps. If I set my machine to 52 pounds and use a soft synthetic string, I'll get about 60 pounds on RacquetTune, and my machine has been calibrated.
Stringing machine and technique have a lot to do with tension. A constant pull machine (drop weight, high end electronic) will give you higher tension than a lockout machine (crank, low end electronic). Also, if you rush to get the job done on a lockout machine (like most sporting goods stores and pro shops do to maximize productivity), your tension will be much lower than the setting. On my drop weight machine, I pull the mains for at least 5 seconds and the crosses for at least 20 seconds (while I weave the next cross). Weaving the crosses increases tension on the mains, which is why I always get stringbed tension higher than my setting.