A Medal Index Card “does what it says on the label” it is card indexed by name that give the medal entitlement and medal roll references for a man [or woman] who served in the forces [incl. Red Cross & Voluntary Aid Detachment] during WWI. The only personal information they give is name, rank, number etc., they do not give age, place or date of birth.

I have not seen a medal from Ancestry but I must assume they are the same as those on the NA's site.

Keeping to men who served in the army, more personal information will only be available [from various sources] for those who died during the war, or if they lived through it in personal records that either survived the WWII Blitz, albeit damaged, or those who’s records were recreated from pension records. Each group represents around 20% of the total of those who served in the Army.

Both sets are available at the National Arcives Kew and on Ancstry [at least the pension records are]. I can't say if the Burnt Documents are yet on Ancestry or how complete either group is.

As for serving in the Cavalry, there doesn’t appear to be any index cards for Moore names that are as good a fit for the ASC one. Search the NA's site for Moore [forename blank] and key word cavalry to see all possibles. Although the ASC used significant motor transport, the majority of supplies were moved by horse transport; the ASC was known as “Ally Sloper’s Cavalry”, so perhaps that's where it came from.