Statistics is the science of gaining knowledge from data. Data are numerical (Quantative) or qualitative descriptions (interviews). Statistics is a method and technique for collecting, processing, interpreting and presenting data. It falls under mathematics, this is mostly quantative.
Statistics is used in many sciences, including politics, economics, psychology, sociology, etc. But the media and society also know the importance of statistics in interpreting or explaining something. It is also used on dialy bases to explain numbers in papers and on the web. A recent example are the COVID-19 data I see everywhere, but also the infographics with which the goverment explains the lockdown rules.
Descriptive statistics is concerned with describing certain data of the population. Think demographics. The data is reduced to key figures that are displayed in tables, graphs and infographics. An example is the CBS data about the amount of COVID deaths or infected people
Inductive statistics tries to obtain data about the entire population from samples. This includes tests, estimation methods and confidence intervals. An example here is the data that is used to produce vaccins. The data is mostly based on a representive sample of the population and not the entire population.
Exploratory statistics is somewhere in between the two previously mentioned. This is based on available data and both descriptive and inductive statistics are applied to this data. An example of this is when there is meaning with the data. I don't only have numbers, but also quotes out of interviews or focusgroups that explains what the data says. Nowadays this is called mixed method. The data used here can be Big Data, when the used data is from old research about something else.
Collecting data for statistics is often done through surveys, interviews, focus groups or measurements. In The Netherlands, the CBS (Central Bureau of Statistics) is a major one in statistics. They collect all kinds of data about the Dutch population (demography, economy, unemployment, consumer confidence, inflation, crime, health, etc.).