Strings & Manifolds: Do Strings Vibrate in 10-11D?

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In string theory are the strings themselves the manifolds? or are the strings vibrating in a 10 or 11-d manifold?.
 
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In old-fashioned string theory (omitting M-theory) one-dim. strings move through a ten-dim. space-time manifold and therefore create a two-dim. string-manifold. The endpoints of open strings are attached to so-called branes which again are sub-manifolds.
 
Strings may also be described as one dimensional branes, 1-brane; that's a reference to one dimensional space, no time component as Tom describes above...
 

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