Steel studs for interior partitions are C shaped and very thin material (see picture below). This means that 16" metal studs on-center actually have room to fit ~16" of material where wood members spaced 16" on-center have space for pretty close to ~14.5" of material in between.
Per the dimensions on the Roxul site in your link, the difference between the wood stud and metal stud versions are exactly for that reason. The metal studs versions are an extra inch wider. Comparing products for 16" on-center spacing: 15.25" for wood studs, 16.25" for metal studs.
You could probably make the metal stud version work for wood studs, but you would need to either:
Compress it by one inch to get it to fit. Compressing insulation reduces its effectiveness, so you will no longer get quite the same advertised R-value.
Cut one inch off of one side along the whole vertical length of every batt. If its faced insulation and you opt for the cutting route, make sure to leave the facing intact so you can still use the facing to secure it to the studs. I haven't seen the metal stud version in person, but I would imagine that the insulation extends all the way to the edge of the facing one one side to fill the void on one side of the steel stud, so this would be the side to cut off insulation.
Personally, I would try to get the right material for the type of framing to make installation easier and/or get closer to the advertised R-value.