PERCENTILE_CONT / PERCENTILE_DISC
Lets recall from statistics that continuous variables (PERCENTILE_CONT) are those that "cannot not be exactly counted," while discrete variables (PERCENTILE_DISC) "have an exact amount."
PERCENTILE_CONT would be better used when performing estimation or predictive calculations, as you are trying to determine a value from a sample of data (where the entire data set is unknown).
PERCENTILE_DISC would be better for when we need an exact measure, and the entire data set is known.
**Note: I am not a statistician, nor an analytics guru, so hopefully someone with greater experience could shine some better light on this, or at least validate my statement.
Hopefully this helps some trying to understand the purposes behind these functions.