Recovery means if you put something into use then collect it after use, how much was collected after use is actually how much RECOVERED. So, recovery percentage is the product of the Obtained (recovered) amount divided by the Expected (how much was used originally) and the whole fraction is multiplied by 100%. To rule out instrument problems in analytical chemistry, we also use a sample of solvent spiked with a level of the analyte that is similar to the spiked level in the sample. Additionally, we would use unspiked sample to make sure that there is no ghost peaks in the unspiked sample.

So, the percent recovery is calculated be [(S2-S1)/C]X100% as you mentioned in your question. Which means, the recovery is [(how much was measured in spiked sample - how much was measured in blank sample)/(how much was measured in spiked neat solvent which is the expected)] multiplied by 100%.

For clarification, the spiked sample S2 represents the amount recovered after you extract the sample. The C represents the expected amount without extraction. Finally, the unspiked sample S1 represent a correction in case your sample originally contains some of the analyte before it was spiked with that analyte.

I hope this clarifies the problem for you.