Co-ordinate is the exact same word as coordinate. As an adjective they can mean to be the same standing or rank, relating to coordination, or relating to an intersection of indices. As a verb it means for things to work or flow smoothly as a group, or to cause things to work or flow smoothly together as a group. And, finally, as a noun, it may mean a part of a set of numbers or symbols used to find a position on a map or graph. Clothing that coordinates are sometimes called coordinates.
While the non-hyphenated spelling is the main entry in both the American and European dictionaries we referenced, it was only in the European dictionary that the hyphenated spelling was listed as an alternative. This suggests that this spelling is going the way of all hyphens.
There is a rare alternative spelling that includes a mark over the second o to indicate the pronunciation (oh oh instead of ew). This is archaic and should not be used.