From the top of the pyramid, I'll try to explain:
Business intelligence (which you didn't mention) is an IT phrase that refers to a complicated system that extracts usable information from data to provide relevant information about a company.
As a result, the goal of BI systems is to provide clean, accurate, and meaningful data. There are no technical issues when the house is clean (missing keys, incomplete data etc). BI systems are also utilized as a database fault checker in production environments (logical faults - i.e.; invoice bill is too high, or inactive partner is used etc). It was accomplished through the use of rules. Meaningfulness is difficult to define, but in simple terms, it's all of your data (even the excel table from the last meeting) organized in the way you wish.
So, the back-end of a BI system is a data warehouse. A database is all that DWH is (instance, not software). It can be kept in a relational database management system (RDBMS), an analytical database (columnar or document store kinds), or a NoSQL database.
The phrase "data warehouse" is commonly used to refer to the entire database described above. There may be a number of data-marts (if the Kimball model is employed) - or a relational system in its third normalized form (Inmon model) known as an enterprise data warehouse.
Data marts are tables in DWH that are related to one another (star schema, snowflake schema). Fact tables (denormalized business processes) and dimension tables
One business process is represented by each data mart. DWH, for example, has three data marts. Retail sales are one, export is another, and import is the third. Total sales, quantity sold, import price, profit (measures) by SKU, date, shop, city, and so on are all available in retail (dimensions).
The process of loading data into a DWH is known as ETL (extract, transform, load). Data should be extracted from multiple sources (ERP db, CRM db, excel files, web service...) Data transformation (clean data, connect data from diff sources, match keys, mine data) Data should be loaded (Load transformed data in specific data marts) edit as a result of a comment: ETL processes are typically built using an ETL tool or by hand using a programming language (python, c#, etc.) and APIs.
The ETL process is a collection of SQLs, processes, scripts, and rules that are linked and divided into three stages (see diagram above), all of which are governed by meta data. It's either pre-recorded (every night, every few hours) or live (every few minutes) (change data capture, triggers, transactions).
Data processing methods include OLTP and OLAP. OLTP stands for "online transaction processing" and is used to transfer data between a database and software (there is usually just one route to input and output data). OLAP stands for "online analytical processing," which indicates there are various sources, historical data, fast select query performance, and data that has been mined.
edit as a result of a comment: Data processing is the process of storing and retrieving data from a database. As a result, the database is set up differently depending on your demands.
Credits for the imagehttp://datawarehouse4u.info/:
The computer technique of detecting patterns in big data sets is known as data mining. Data mining can provide you with a more detailed perspective of a business operation or even a forecast.
In the area of business intelligence, analysis is a verb that refers to the ease with which you can extract the information you need from data. Multidimensional analysis describes how your data is sliced by the system (with dimensions inside the cube). According to Wikipedia, data analysis is the process of evaluating data in order to identify usable information.
Analytics is a term that refers to the outcome of an analysis process.
Don't make such a big deal out of just two words.