The reason I remember for the different names and engines on the AS350 was because in order to import a foreign built helicopter into the US, it had to have a certain percentage of its parts manufactured in the US. And the easiest way was to use a US made engine. Hence the use of the LTS-101 in the Astar. Same for the USCG Dauphins I think.
Eventually the law went away and I can remember getting the 1st AS350B into the shop. We were intrigued the engine lasted so long.
As for the "falling star" name, it actually started with the sun gear issues in the main xsmn. However, after the fleet wide fix of the gear the 101s started to puke turbine disks regularly and the nickname came back with a vengeance.
I think between the all the 222s and 350Ds we operated then, there was a LTS-101 being changed every other day for awhile.
W1