The ICAO term is "visual manoeuvring (circling)" for what is called a "circling approach" in the US. That is not the same as a "visual approach". Both would, at least in my estimation, be construed as VISUAL CHANGES OF LANDING RUNWAY for the purpose of hetfield's question.
Actually, that is not the case.
A circling approach is relatively well defined. A clearance is given for a specific approach, e.g., "Cleared VOR 13 Approach, circle to land Rwy 18." In that case the missed approach procedures for the VOR 13 Approach are still in effect.
In a late-breaking "Do you want 25L instead of 24R?" situation (assuming VMC), the approach to 24R is terminated, and a visual approach to 25L is commenced from that point. There is NO clearance to "intercept ILS final for 25L" or similar, therefore it is a VISUAL approach from the point it is accepted, and there is no defined missed approach procedure (excepting the airport-specific cases such as the general lost comm procedures for LHR).
Again, it is ALWAYS the responsibility of ATC to provide specific missed approach instructions in the latter case, and in the former case if they do NOT want you to do the missed approach per the VOR 13 procedure.