Not all square-taper is the same, based on the question that you're asking.
First, there are two square-taper standards, ISO (Campy and Stronglight, and - randomly - Sugino 75's) and JIS (Japanese and most others). The ISO taper is slightly smaller, although they share the same taper angle.
This does not mean that tools need to be different.
Tools for removing square-taper cranks from the bottom bracket are all practically the same - doesn't matter brand or taper standard.
But as to your question: tools to install or remove the BB into the frame's BB shell do differ by brand and often within brands, especially with cartridge BB's. However, Shimano and Sugino's cartridge BB's have the same interface, as does Tange and plenty of others.
It may be that the Shimano interface is totally common now, as seely says. I've got a Campy sealed-cartridge BB from 2000 (Mirage 9-speed triple gruppo) and it's got a completely different interface, takes a different wrench.
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"c" is not a unit that measures tire width