is new castile the same as Castilla-La Mancha?

Answer 1

No.

Castilla-La Nueva used to be a province or formally recognized region of Spain. It included La Mancha and other territories. It was separated from Castilla-La Vieja by the central mountain range. Both were part of the Kingdom of Castilla.

The name is shared with a region in Colombia.

Here's a nice, old map: http://www.uam.es/personal_pdi/ciencias/depaz/mesa/default2.htm (pause to let it load - takes a few seconds even on broadband).