English surnames began to be adopted in the 14th century, partly for reasons of taxation. The vast majority fall into four categories: habitation names (the villages, towns and cities where people were living), occupational names (their jobs, although many are not obvious), ‘son of’ names (those ending in ‘son’) and, less common, various animals, particularly birds and fish. Rarer are those that suggest a physical feature, such as Copper for someone with red hair.
Hands probably has several origins, including the Dutch word Han or Hans, or someone with large hands, or someone who used their hands in their profession and where it was originally a nickname. The only significant variant I have come across is Hand singular.
Cheesman is easier as it’s obviously an occupational surname. Most commonly spelt without an E in the middle, you do sometimes find the alternative spellings Cheeseman, Chesman, Chessman, Cheseman, Cheesmond, and Chisman, all of which are probably phonetic variations. A number of my ancestors’ public records use the spelling with the middle E.
There is a useful tool on the Ancestry website which shows the distribution of surnames in England and Wales in 1891. The highest concentration of people with the surname Hands was around Oxfordshire, while for Cheesman the distribution is concentrated in Sussex and Kent, with Surrey and Hampshire not far behind.
As has often been said, widespread illiteracy prior to the 20th century meant that many people did not know how to spell their own names and officials in the church and Registry Offices around the country did little better.