Descriptive statistics only describes the data, so you would use it only if you were interested in the properties of you data... which is rarely the case if you have a sample, unless your sample is your population, in which case this makes more sense. Descriptive statistics should more often than not be used if you have population data.

While inferential statistics would be used on a sample, to infer the properties of the population.

All is well, except that some people will argue that you never really have data for your whole population or that you have incomplete data for various reasons: changing population, measurement error,... and so these people would argue that it is better to use inferential statistics even with population data.

A population does not need to be big, the population is what you choose it to be. If you are studying students in a specific class (and you are interested in these particular students), and there are 30 students in it, then this is your whole population.