When about a VMC approach I think you are referring to what used to be called 'approach maintaining VMC and own separartion'. I don't think this has been used in the UK for several years but ICAO describes it in PANS-ATM para 5.9 as below:
CLEARANCES TO FLY MAINTAINING OWN SEPARATION WHILE IN VISUAL METEOROLOGICAL CONDITIONS
When so requested by an aircraft and provided it is agreed by the pilot of the other aircraft and so authorized by the appropriate ATS authority, an ATC unit may clear a controlled flight, including departing and arriving flights, operating in airspace Classes D and E in visual meteorological conditions during the hours of daylight to fly subject to maintaining own separation to one other aircraft and remaining in visual meteorological conditions. When a controlled flight is so cleared, the following shall apply:
a) the clearance shall be for a specified portion of the flight at or below 3 050 m (10 000 ft), during climb or descent and subject to further restrictions as and when prescribed on the basis of regional air navigation agreements;
b) if there is a possibility that flight under visual meteorological conditions may become impracticable, an IFR flight shall be provided with alternative
instructions to be complied with in the event that flight in visual meteorological conditions (VMC) cannot be maintained for the term of the clearance;
c) the pilot of an IFR flight, on observing that conditions are deteriorating and considering that operation in VMC will become impossible, shall inform ATC before entering instrument meteorological conditions (IMC) and shall proceed in accordance with the alternative instructions given.
So the key difference is that with a visual approach ATC provides sepaarartion whereas during a 'VMC approach', where it is allowed, the pilot provides the separation/collision avoidance.