Help understanding water softener and hardness

The house we are in had a softener when we arrived, though it was bypassed. Original to the house, so 25 years old. We immediately noticed the soap scum and signs of hardness. Was thinking maybe not worth getting someone to get the original up and running, and instead just install something new.

We bought test strip and found somewhere between 3 and 7 gpg or 50 to 120 ppm.

But when looking at softeners they all seem to be measured in grains. Like 50,000 grain. I can't seem to find anything that explains the relationship between these things.

I'd like to give the install a shot on my own. Assuming I find out what size we need.

Thanks