Is this what I'm looking for in order to replace a hose that connects my transmission to the radiator?

I sort of cut the hose off the old one on a radiator replacement. Now I’m leaking transmission fluid.

Is this what I’m looking for in order to replace the “cooler line”?

O’Reilly Link Here

Is it even called a hose? Or cooler line? Or tube? I just need to connect my automatic transmission to the radiator. Thanks!