These product descriptions refer to the size of the coal pieces and not the quality.
Coal, which is also sometimes known as Trebles or Cobbles, tend to be pieces between 40mm and 100mm in size, whilst Doubles are between 20mm and 40mm and Singles between 14mm and 22mm.
You will also see certain products referred to as Beans, Grains and Nuts, which is again in reference to the product size and are used specifically in certain appliances for the uniformity of their size.
When choosing the right fuel for your open fire, a lot of the time it will come down to your own personal preference on whether you choose to burn large pieces of coal or if doubles suit your fire better.
Depending on the size of your multi-fuel stove, you may find that doubles are better suited as it is easier to fill.
Singles work best in certain boilers or alternatively, you may use Singles or Slack to extend the life of your fire or to tame a roaring fire.