If you look further down the message forum, you'll see that I have also queried these Cutlers entries - and several folk have done their utmost to help me out! But my problem then was to try to disentangle the meanings of the numbers at the end of each entry.
If you scroll up the lists to the very first page, you'll find a list of the abbreviations used which will help you out a lot
As I recall - not very good at getting on and off pages so daren't go back to the abbreviations right now ! - I would say that Henry Machon of Colly Elms was a cutler and my best guess is that John s/o John Maxfield would have been apprenticed to him for 8 years starting in 1678. I tentatively suggest John s/o John would have aimed to have finished his apprenticeship at the age of 21 (or thereabouts) so he might have been born roughly c.1665 so your relative 1665 - 1712 would fit here nigh on perfectly
The second line of Johns is a puzzle. I would maybe suggest that they have 3 different Johns here, with just maybe your John b. 1705 gaining his Freedom in 1728 - the John b.1730 gaining his Freedom in 1751 - and where the third John s/o Thomas comes in ....??? Pass!
Paul 1769-1821 would have been 14 in 1783 - perfect age for him to have been app. for 7 years and finished by the age of 21 Etc.
Incidentally - I've done some work on my cousin's husband's family for him and have got as far back as the marriage of Thomas Maxfield to Ann Whitaker at Sheffield St Peter's 1798. Their son Henry b.1805 married Ann Boocock at SSP 1831 and their great grandaughter Hilda Emily Maxfield 1904-1989 was Peter's mother. Any connection with your Maxfields I wonder idly ....
Anyway, I hope the page of abbreviations and the answers I received a month or so ago help you out.
Thanks for all the information. It looks like there is a connection. I have the same information for Thomas and Ann Whitaker. He is my 3rd great grand father and Henry is his son born about 1805 but this varies slightly in different sources. At the Sheffield Archives I found a marriage entry for him and Catherine Stillings who appears as his wife in different censuses. In my tree i have a Hilda Lillian Maxfield born in 1912 who is my first cousin once removed. Does this help you to make a connection?