The death entry in the Dec 1942 appears to be indexed (on FreeBMD) under three different names ...Minnie F L FOX, Minnie F LORING-FOX and Minnie F HILL, which will reflect that her name appears as such on the death entry (probably as "otherwise" or "also known as" or "formerly known as").
On the new GRO index, the DEC entry only appears as Minnie Frances HILL which suggests that is the first name that appears on the register entry.
My guess would be that the first entry, in the JUN quarter, only recorded her name as LORING-FOX, and for whatever reason it became important to get that changed. Rather than a correction it appears to have been done as a full re-registration.
The re-registration in Dec would have led to a note being added to the margin of the earlier JUN entry, which would have triggered the submission of an Occasional Copy of that one.
As already mentioned - different indexes are compiled using different rule sets and it is to be expected that the results will differ and it can actually be useful sometimes.
A mismatch between the printed index (as used by FreeBMD), and that in the GRO on-line index will very rarely be an error, just a reflection of the different rules being used.
But there are always other explanations possible - so to be certain, you would need to order a copy of a certificate from each entry and compare them.
