Coming from a behavioural sciences background, I associate this terminology particularly with introductory statistics textbooks. In this context the distinction is that :
- Descriptive statistics are functions of the sample data that are intrinsically interesting in describing some feature of the data. Classic descriptive statistics include mean, min, max, standard deviation, median, skew, kurtosis.
- Inferential statistics are a function of the sample data that assists you to draw an inference regarding an hypothesis about a population parameter. Classic inferential statistics include z, t, $\chi^2$, F-ratio, etc.
The important point is that any statistic, inferential or descriptive, is a function of the sample data. A parameter is a function of the population, where the term population is the same as saying the underlying data generating process.
From this perspective the status of a given function of the data as a descriptive or inferential statistic depends on the purpose for which you are using it.
That said, some statistics are clearly more useful in describing relevant features of the data, and some are well suited to aiding inference.
- Inferential statistics: Standard test statistics like t and z, for a given data generating process, where the null hypothesis is false, the expected value is strongly influenced by sample size. Most researchers would not see such statistics as estimating a population parameter of intrinsic interest.
- Descriptive statistics: In contrast descriptive statistics do estimate population parameters that are typically of intrinsic interest. For example the sample mean and standard deviation provide estimates of the equivalent population parameters. Even descriptive statistics like the minimum and maximum provide information about equivalent or similar population parameters, although of course in this case, much more care is required. Furthermore, many descriptive statistics might be biased or otherwise less than ideal estimators. However, they still have some utility in estimating a population parameter of interest.
So from this perspective, the important things to understand are:
- statistic: function of the sample data
- parameter: function of the population (data generating process)
- estimator: function of the sample data used to provide an estimate of a parameter
- inference: process of reaching a conclusion about a parameter
Thus, you could either define the distinction between descriptive and inferential based on the intention of the researcher using the statistic, or you could define a statistic based on how it is typically used.
A very good question, and a question that I myself had because I have heard these called buckets, groups, groupings, categories, categorical variables, discrete variables, and bins as I have changed disciplines. In general, use the language that the end-users of your analysis are most comfortable using - in a sense, speak their language (or force them to use yours! ha). There is no wrong answer here, other than a countless number of statisticians that would say that you shouldn't be grouping your variables into bins/buckets without a very good reason (or ever!) as you are spending degrees of freedom, making arbitrary cutoffs to create your buckets/bins, and losing information that was provided by your once valuable, continuous variables.
Best Answer
A simplified view may be as follows:
Suppose the objective of the survey is to estimate the per household income of $abc$ national in a city. Then the all the households of $abc$ nationals is the the target population. It is the collection of items from which a sample has to be taken.
A sampling frame is a list of the items of the population from which a sample is to be obtained. Suppose a household list of the city is available. This list of households become the sampling frame.
This list may contain households of other nationals. These households are not eligible items for being members of the population. They need to removed before a sample is made.
The sampling frame may not contain all the households of the $abc$ nationals. In that case, some eligible items of the population are left out from sampling.
When contacted, some households may refuse to provide information.
The remaining households in the sampling frame become the actual sampled population.
I an ideal situation, the population and the sampling frame are same.