I know they are four different areas, but I would like to know what are the main differences between those disciplines, and how they are related to each other, if some of them depend on each other, and what is the specific objective of each one.
The simplest way to explain:
Big data is essential the data itself. It is "big" because of the size and scale of it. You can think of this as the datasets that are composed up of hundreds of thousands or millions of observations. With more people online, more data is generated and this is what people mean by big data.
Data warehousing is the storage of all of these massive amounts of data. You can think of this as the place where big data is stored. This can be on large servers or large databases or even in the cloud.
Business intelligence is the use of big data (or small data) to draw insights that could be useful for making business decisions or applications. This is essentially leveraging the data to help improve aspects of a company.
Data science is a very broad term that can encompass topics like ML, data analysis, Artificial Intelligence, statistics etc. There is no one specific definition but more generally can mean anything having to do with working with data these days.