Just to note, Ancestry have transcribed him as F H on 1871, rather than T H as on the Familysearch link, which looks correct from the image. He's also a painter not a packer
1861 - Frederick H Williams b Cheltenham, painter and decorator, with wife Elizabeth and children Elizabeth 1 and Martha 1 month
marriage 1859 - Frederick Henry, spouse Elizabeth Holloway His father is Mark - so perhaps he's a relative of Thomas William given the latter calls his son Mark?
Added: there's a number of baptisms matching the birth registrations you listed, parents Frederick Henry and Elizabeth
