What’s the difference between tamari and soy sauce

I have a bottle of San-J Tamari (black label) in my fridge and the back reads:

Tamari is a premium soy sauce made with more soybeans than ordinary soy sauce giving it a richer, smoother, more complex taste. Tamari has more flavor enhancing properties than salt. Add 1 tsp. (320 mg sodium) instead of tsp. salt (590 mg sodium) to reduce sodium intake. Stir-fry or marinate poultry, meat fish and vegetables. Add 1-2 tsp. to perk up sauces, soups, gravies and casseroles.

In my experience, I use a little less tamari when substituting it for regular soy sauce. As Sean mentioned, it's definitely a bit stronger than regular soy sauce. I eyeball most of the time, but I'd say I use 1/2 to 3/4 portion of tamari when substituting it for regular soy sauce.

I reach for the tamari when I want a bit more of a complex flavor on something plain like rice - when the soy sauce is to be the star of the dish, essentially. I tend to use regular soy sauce when mixing into a larger homemade sauce or where the soy sauce flavor will blend into the background because the recipe calls for so many other strong ingredients.

Oh, and tamari seems to add a bit of an almost "smoky" flavor, it seems.