Anne,
I would imagine (on no basis whatsoever!!), that they were actually baptised in the Beaverlee Schoolroom Primitive Methodist chapel at Beggarlee but that this chapel (or the clergyman who performed the ceremony) was part of the Ilkeston Primitive Methodist Circuit and so the record happened to be entered into both registers.
I know very little about Derbyshire and/or Nottinghamshire geography but I see from Genuki that both Greasley and Ilkeston were taken in under the Registration District of Basford from 1837 when statutory registration began.
A search on Google for Beggarlee (also some of the other names/places) turns up lots of interesting stuff - including passages from "Lady Chatterley's Lover"!
I guess you noticed IGI entries (LDS) for Lettice's christening and death (2 Sep 1792 and 14 Jun 1872), parents Francis SAXTON and Hannah HOURS. And an extracted entry for the marriage of Francis and Hannah in Greasley 18 Jun 1787. And other submissions for children of theirs, etc, etc
Ancestral File at FamilySearch gives details for a submitter of Francis SAXTON - these may be long out of date but often worth a try. There's also an entry in the Pedigree Resource File section with the name and address of a different submitter.
Who knows what you might find in the films of the actual church registers - either in SLC or ordered in to your local LDS FHC.
Good hunting,
JAP
