I've just got back some certificates and you did ask about them!!
Mary Jane Wood born in 1857 shows parents James Wood and Eliza Wood formerly Care, living at the Strand Rye which fits in with the 1861 census.
Mary Jane's marriage certificate shows surname Brettwood and a witness with the name of Care
The birth certificate of MJ's daughter (my grandmother) shows the mother's maiden name as Wood, not Brettwood.
Marriage certificate of James Henry Wood shows him married to Eliza Ann Care. Now interestingly, James has not father listed which I assume means he is illegitimate.
Now that might explain the difference in surname - maybe Wood was his mother's name and maybe his father was called Brett so he added it to his name at some point - could be his mother's deathbed confession

I don't know, but it now opens up a fascinating line of enquiry - so thanks again for getting me started on this.
Hils