There seems to be a systematic ambiguity. The quartiles are the three values that divide a probability distribution into four parts; but loosely, "quartile" is also used for any one of the four parts so created.

The only terms I've seen are quartile, decile, and percentile, and I think these are all subject to the same ambiguity. People talk of something being in the top percentile, meaning it's in the top 1%. Strictly this is above the top percentile, which is the 99th percentile.

If n is an integer, an n-ile is a value that divides the data into n equal parts, so there are n - 1 n-iles altogether. The first n-ile separates the lower 1/n from the remaining (n - 1)/n. So the first quartile separates the lower quarter from the upper three-quarters, the middle quartile separates the upper and lower halves, and the upper quartile separates the lower three-quarters from the upper quarter.

Those quarters are also loosely referred to as quartiles, under the natural (mis)apprehension that there must be four quartiles.

If q is a proportion 0 < q < 1, the q-quantile is the point such that the amount of data under it is q. So the first quartile is the 0.25-quantile.

As quartus is a Latin ordinal, and as the old month names were Quintilis and Sextilis, probably "tertile" is a good name for the two points dividing data into three.

http://www.riskglossary.com/articles/quantile.htm