I'd never even heard of Fold3 until you mentioned it, so I searched for my grandfather's military records (he enlisted 1901 and was discharged medically unfit in 1906) and sure enough it's in Fold3. However, although the transcription of the description of his records needs a lot to be desired (it was OK when it was on Ancestry) such as Noly Henity York - for Holy Trinity, Yorkshire and Hussars Jthe Lene - for Hussars 19th of the Line, the other difference is that his records are listed as being in the Royal Hospital Chelsea Pensioner Soldier Service record. Where that has come from I have now idea, he was never a Chelsea Pensioner and when discharged medically fit he was discharged to a mental hospital. Mind you he was out within 6 weeks working as a classical musician and getting married less than a year later.
Modified - Of course his records are available on FindMyPast and without taking out a free trial with Fold3, it looks as though they are the same records, whatever the title is on Fold3. As it happens, I have a copy of the records from TNA.
