I have never thought of such a distinction between "bits" into "data bits" and "switching bits".

From a circuit perspective that makes kinda sense, but from the abstract "bit" perspective, the "switching bit" is a mechanism that operates on bits which in the end are also data. In other words there is only one type of bit: the data bit, and the switching comes on top of it.

> Voltage is made out of flow of positive electric charges.

Not really. What usually flows (in metals) are electrons. Quarks stay where they are. And when we prefer to think about flow of positive charges, the positive charge in question is a hole left by a missing electron. Physically real positive charges (ions) can flow in electrolytes though.