Collar ties go on the top third of the rafters, and mainly hold the rafters to the ridge beam, they may or may not be required by local code, or may not be required if you use an approved metal connector like a Simpson rafter tie.  

Rafter ties go across the bottom third of the rafters, in older construction they could be on the bottom half or bottom two thirds of the rafters.  They prevent the roof from flattening, and they're pretty much always required.  In most cases ceiling joists serve as rafter ties.