1. French and English from Latin "a Moor". Introduced to Britain by the Normans.
The preferred spelling in the Middle Ages was Morris but Maurice was more popular when it made a come back in the 20th century. It occurs very rarely in the 1841 Census of Aberdeenshire. Other spellings are listed, above.
In old documents in Latin, the form Mauritius may be used, with appropriate case endings.
2. The Irish Celtic name Muirgheos - "sea choice" - is Anglicized as Maurice. The Irish Gaelic variant is Muiris.