Its interesting that the estimated birth year on the census both say 1810 and yet the information I have says 24 May 1809. I know its only one year but you'd think she would know what year she was born. Was the census filled out by the residents?
The census only records the ages (whole years), it's the transcription sites who add the year of birth which can be out if their birthday is after April that year.
Head of each household was responsible for filling in a census return. A census enumerator delivered a blank census form to every household in his district before census day. He revisited every property after census day to collect a census return from each household. If nobody in a household was unable to fill in a census return for some reason (e.g. illiterate, vision-impaired, arthritis in hands, no pen or pencil) someone they knew may have done it for them, or, failing that, the census enumerator would have completed the form.
Next task of a census enumerator was to copy information from household returns into a census enumerator's book for his area. This involved deciphering handwriting of many people, including perhaps names of unfamiliar birthplaces.
Majority of 19th century household returns for England no longer exist. Transcriptions on websites were made from census enumerators' books. Therefore they are transcriptions of transcriptions, so twice-removed from the original household census returns.
If you look at an image of a census enumerator's book you'll notice that ages were in years. As Rosinish said, transcription sites calculate years of birth from those ages but they are only estimated years of birth.
Census Day in England in 19th century was usually in March or April, except 1841 which was June. A person whose birthday was March or April may seem to have aged by 9, 10 or 11 years between one census and the next. The apparent discrepancy may be due to whether their birthday was before or after census day that year. Census day 1921 in England was in July. One of my grandmas had aged 11 years since 1911 census because her birthday was in May.
Not everyone in 19th century knew their exact age. Some probably knew their real age but didn't want other people to know e.g. a woman with a husband younger than her.
Census enumerators for 1841 census were supposed to round down ages of adults (people over 15) to a multiple of 5 years. Some census enumerators complied with the instruction, some didn't.
