It seems clear that that the name Manns is most often German, and occasionally Jewish, and that Mans is a Dutch surname.
A famous bearer of this surname was Sir August Manns, who was born in Pomerania and went to Britain in Queen Victoria's reign, becoming a famous musical conductor. He died in 1907.
I've recently discovered information that might be helpful to people researching English ancestors called Mans/Manns. The name doesn't appear to have any links to the Germanic/Anglo-Saxon word "mann". The presence of the double n (and of the final s, which makes the name appear to be a possessive or patronymic) has only served to obscure the fact that probably most English (as opposed to German, Dutch, or Jewish) people with the surname are descended from immigrants from Le Mans (birthplace of the first Plantagenet king, Henry II, and held by his father, the Count of Anjou) in France to the Welsh Marches (especially Hereford)during the 1100s when the Normans were populating the Marches with their followers. At that time Le Mans (now capital of the Sarthe) was in the French province of Maine, owned by England until 1204. Two of these immigrants, Matthew de Mans and Simon de Mans, were knights ("militaris"). All these people called de Mans (sometimes written de Mauns) were landowners in the Hereford, Worcester, Gloucester regions. That would explain the prevalence of the quite rare English name Mans/Manns in those regions (especially Gloucester) today. The de Mans family are mentioned in medieval records published recently in the ongoing Victoria County History of England series and other academic sources. Some are already online. Google the following individuals (it helps to put the names beween quotation marks): Simon, Matthew (two separate men), Walter, William, Richard, Gilbert de Mans and you'll see what I mean. In a few cases (e.g. Richard) they appear as de Mauns. But this is really de Mans (Frauncis for Francis was a similar medieval spelling). Possibly there are other de Mans individuals in records not yet online. Don't forget the del Mans spelling too - this appears in medieval Latin records!