German French (Norman) and English, from Old German "mighty in battle".
The name Matilda was introduced into Britan when William I ["the Conqueror"] married Matilda of Flanders.
Maud may be considered as a synonym or derivative, or possibly a diminutive. Old documents in Latin used Matilda, with appropriate case endings, for Maud as well as for Matilda. Maud remained in common, spoken use but Matilda was very rare from medieval times until its revival in the late 18th century.
In the 1841 Census of Aberdeenshire Matilda occurs frequently but Maud does not. Other very rare spellings in that Census are Mathilda and Matelda.
Note: Edith, daughter of King Malcolm II of Scotland, was also called Maud or Matilda, but these are not known to be generally synonymous with Edith.