I am not understanding the difference between quarrying ans shaft mining.
A quarry is generally an open pit mine. This is where the "over burden" or surface materials are removed to get to the minerals that are wanted. This material is then removed using large machines and heavy trucks to remove the ore. The ore is then taken to a processing facility to remove the desired minerals like gold, copper, iron etc... IT may also be used to mine coal, or building materials such as clay, limestone and granite.
A shaft mine is "drilled into the earth to reach the desired layer with out the removal of the over burden. The minerals are then mined via shafts drilled horizontally in what are called "galleries" this then leaves pillars of material in place to hold up the over burden. This form of mining can be very dangerous due to the potential for collapse and trapping miners inside. However, this is the preferred way to mine for materials that are very deeply buried. Gold in South Africa is very far below the surface of the ground and open pit mining would be very impractical, so it is done with shaft mining.
Open pit mining leaves very ugly scars on the surface of the Earth and these are unpopular due to the damage seen on the surface. On the other hand some shaft mines, especially for Coal has caused irreparable damage to the environment our to the coal catching fire and burning for years underground causing much damage.