I think you have slightly muddled 2 concepts, Weather conditions and VFR minimum conditions.
The USA use 4 levels of weather description. From worst to best they are LIFR>>IFR>>MVFR>>VFR
The definitions are given in the FAA AIM as:
1. LIFR (Low IFR).Ceiling less than 500 feet and/or visibility less than 1 mile.
2. IFR.Ceiling 500 to less than 1,000 feet and/or visibility 1 to less than 3 miles.
3. MVFR (Marginal VFR).Ceiling 1,000 to 3,000 feet and/or visibility 3 to 5 miles inclusive.
4. VFR. Ceiling greater than 3,000 feet and visibility greater than 5 miles; includes sky clear.
If you look at something like sjyvector(https://skyvector.com/) or foreflight (Ozrunways equivilient) then they color code an airports conditions from Pink>>Red>>Blue>> Green. It gives you a very quick overview of the conditions at an area or along your route. It is also useful for setting personal minimum above the legal minimums. While it is legal to fly in MVFR conditions as a VFR pilot many people choose not to.
A special VFR Clarence is a clearance given by ATC that allows a VFR pilot to fly in conditions that are below the normal VFR minimums of 91.155. For instance in class D airspace the normal VFR minimums are 3 Statute mile visability, and distances from cloud of 500 feet below, 1000 above and 2,000 feet horizontal, In class G airspace below 1'200 feet AGL the requirements are 1 statute mile and clear of cloud.
Now if you wanted to take off from an airport where the ceiling was 1300 feet. If you were at a non-towered airport you could takeoff, climb to 1'000 feet and depart on your way. If the airport had a control tower and was class D you wouldn't be able to climb to 1000 feet and fly off. A special VFR clearance allows you to operate where the viability is 1 statute mile and you are clear of cloud, essentially the same as the class G airspace requirements.
The above is all based on the USA rules and regulations. The Australian rules are similar but with some subtle changes.