Basically a tack rag is a tack rag but there are differences.
First, what decides how effective the tack cloth works is how "tightly wound" the weave is. The smaller the little squares and more squares per square inch the better the grade.
Next concern is the amount of glue used, if you are cleaning saw dust off of wood a blue tack cloth make for clear-coats with less glue is not going to work very well.
Will it work on your car? Yes if you are careful.
There are a lot of different grades of tack cloths made but the variances come down to the glue and weave.
Auto manufacturers are very picky about the the weave and usually the ones they buy are special made for them, as that type of weave would drive the cost up too high for selling in the "automotive refinish market"
OEM plane manufacturers are the same way and one I know have their own test before anyone is allowed to use the tack cloth.
They break the cases down by batch numbers and an engineer will take a tack cloth from each batch, lay it on a piece of metal and lean on it for 30 seconds, if it leave glue, they won't use it.
I would go to an autopaint store and pick one up.