You need a JWS-3309, or Toyota T-IV spec fluid. (I know you're already aware.) Are they all the same? Don't know, haven't tried every brand...
What I can say, is that I've used Toyota T-IV, MOBIL 3309, AMSOIL Signature Series, and Valvoline Import multi-vehicle with success in my P2 Volvos (AW-55).
I've never used the Volvo fluid - at nearly $30/quart, for a mineral oil, it's outrageously priced. The Toyota T-IV is identical.
Picking up a case of T-IV at the Toyota dealer is both convenient and a decent deal. That's my recommendation.
If you ever start to have the shift problems for which the '01-'02 AW-55 is known, PM me - I've done valve body surgery on all three of mine. Most recently, I swapped a brand new GM Valve Body*, bought on Amazon for $495, into the '01 V70. A slight modification to the wiring harness was needed, and I had to swap the S4 solenoid from the old VB. A reasonably cheap fix for an AW-55 with shifting issues.
*Some GM cars and some NIssans also used the AW-55, though GM called it the AF-33. So, GM still has valve bodies for sale. The key point of failure on the early valve bodies was the bore for the SLT solenoid, which controls line pressure. Bore wears, allowing fluid to leak resulting in low line pressure. With low line pressure, the transmission starts acting up. Various kits exist to fix this problem, and many companies rebuild that particular body with a sleeve kit in the SLT bore. The GM body is new manufacture, and doesn't have the problem. At $495, it's cheaper than rebuilding the old body. A quick programming and drive adaptation is needed for the install.