TOPIC: Technical name

I know this is to stop rafter spread, but I can't remember the name for these. It is in a garage, the first 2 rafters only.

Would cable tie downs be appropriate?

Because they're made from cable, I guess I agree with David and would call thhem collar ties. If they were made of wood... and what should be there instead of the retro fitted cable ties are called "collar ties."

I have heard them called "metal straps," and "coil straps," ostensibly to prevent the bottoms of the rafters from spreading outward.  A collar tie should be up withing 4' of the apex of the roof, intending to keep the roof from spreading upward or outward.  If they are near the middle of the rafter they become unstable. 

Two problems with this post-facto strap application that is pictured above:  they can be tightened too much and force the roof upward (!) and do not have much wind load resistance.

Were they on the edge or in the center of the garage?  Maybe someone removed the original truss structure because they wanted a storage loft or something?  Depending on what the guy wanted to do, perhaps to prevent sagging in the middle of the roof at those rafter points, a scissor truss may have been a better installation.

Jay is right, a coller tie is located closer to the apex. It would be a ceiling joist

I saw that pic on the Nachi Board.
I think my response was that this garage, shed or what not, is old, has a low pitched roof, and they used an oversized 1/2"+/- steel cable to pull it back together. Probably no rafter ties or collar ties.
That cable is oversized for those puney turn buckles with open ends on them and whoever installed those cable clamps had no idea the amount of tension there was going to be.
The cable clamps are backwards,  you never saddle a dead horse on a steel cable.
It would be my guess that the weight of the cable is doing the job of acting as the rafter tie.