Is this the same as the 4.3/4.4mm SHM wrench?

No — the 3.75/3.96mm and 4.3/4.4mm versions cover different Shimano nipple sizes. The 3.75/3.96 covers certain road and entry MTB builds; the 4.3/4.4 covers many road and MTB wheelsets. Check your wheel spec.

Can I use this wrench on non-Shimano spokes?

Only if the nipple size matches exactly — 3.75mm or 3.96mm. The Birzman range also includes DT Swiss-specific and generic spoke wrenches for other sizes.

Birzman

Birzman 2-Ended Spoke Wrench 3.75/3.96 (SHM)

Name: Birzman 2-Ended Spoke Wrench 3.75/3.96 (SHM)
Brand: Birzman
SKU: CMB_WOW_BM20-DSW-375/396_Std
Price: 1510.00 INR
Availability: InStock
Author: InstaSport Editorial

₹1510.00

Description

The Birzman 2-Ended Spoke Wrench 3.75/3.96 SHM targets the smaller Shimano nipple sizes found on certain road and entry-level MTB builds. Like its sibling, the dual-ended format places the right jaw size at each end, eliminating the need for separate tools. Chrome vanadium jaws machined to Shimano t