In the Wikipedia article about test statistic it is written
A test statistic is a statistic used in statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.
while the Wikipedia article about descriptive statistics states
A descriptive statistic is a summary statistic that quantitatively describes or summarizes features of a collection of information.
It seems to me that both statistics are a means to summarize the given data (e.g. a sample of a population), but, depending on the context (i.e. hypothesis testing or descriptive statistics), we use one expression rather than another. Is this correct? What are the differences between them?