The sure way is to pull the muffler and look at the piston/rings. A chromed piston (in a bare aluminum bore) with two THICK rings means a 3400 or 3800 (and you can differentiate between those by measuring the bore). A bare piston (in a chromed bore) with two thin rings means a 3700 or 4000 (which again differ in bore). Since that saw's a grey/black rather than red/black Craftsman saw in this series I can assume that the saw is a 3400 or 3800 (as long as the saw is as it came from the factory)....................as Sears didn't sell any grey/black 3700's. Sears had transitioned their 3.7 saws from 3700's to 3800's during the red/black production period.
A red/black Craftsman in this series could be a 3400, 3700, or 3800. The red/black 3800's have a very different 358.xxxxx Sears model number compared to the red/black 3700 saws. If you look up the saw on the Sears partsdirect.com site using its 358.xxxxx model #, you can find the part #'s for the piston, cylinder, and rings. You can look at the 3400, 3700, 3800, and 4000 IPL's (or a Poulan pistons/cylinders index if you have 'em) and determine which saw it is that way.
Now..................somebody could have installed a top end from any saw in this series (3400-4000 and PP375/385/395) sometime along the line (it's been done)..............and that's why the only sure way to identify what we have here is by pulling the muffler, looking at the piston/rings, and measuring the bore.
For some reason......................sellers of these saws almost always list them as a "Craftsman 3.7, same as 3700" (or similar), even when they're grey/black. Either they don't know about 3800's, or they just assume that the saw is a 3700 because it's a 3.7 rather than a 3.8 (Sears never labeled them 3.8).