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I'd say it's it's definitely the same hand. Could be a handwritten copy of the original.

Ancestry has this database "UK, Registers of Births, Marriages and Deaths at Sea, 1844-1890"

Two John Patterson's died at sea in 1861
One on the ship Lena, died off Lowestoft 5th Sept 1861
The...

Looking at the 'evidence' presented (particularly her children having MMN Ramshaw) it looks like the registrar in 1862 transposed her maiden name and married name, it happened! It's likely Mary Ann...

RAMSHAW, MARTHA HUMBLE
GRO Reference: 1839 J Quarter in DURHAM AND LANCHESTER Volume 24 Page 64

I think this is them in 1851 with surname mistranscribed

HO107; Piece: 2394; Folio: 98; Page: 14;
Living Great Lumley
John Ramsher 58, Coal Miner, Northumberland
Sarah Ramsher 53, Durham...

These baptisms also took place at Houghton le Spring, parents John and Sarah Ramshaw

Margaret 16 Jun 1834; Jane 6 Aug 1832; Martha 3 Feb 1831

From Family Search. https://www.familysearch.org/ark:/61903/1:1:N58C-661

Name: Mary Ann Ramshaw
Gender: Female
Christening Date: 17 Sep 1836
Christening Date (Original): 17 SEP 1836...

Mary Ann's children seem to be registered with Mother's maiden name as RAMSHAW, for example

PEAT, SARAH JANE RAMSHAW
GRO Reference: 1867 J Quarter in SUNDERLAND Volume 10A Page 540
...