You should not rely only on CAP theorem. There is ACID principles, which
describes a set of properties that apply to data transactions:
Atomicity - Everything in a transaction must happen successfully or none of the changes are committed. This avoids a transaction that changes multiple pieces of data from failing halfway and only making a few changes.
Consistency - The data will only be committed if it passes all the rules in place in the database (ie: data types, triggers, constraints, etc).
Isolation - Transactions won't affect other transactions by changing data that another operation is counting on; and other users won't see partial results of a transaction in progress (depending on isolation mode).
Durability - Once data is committed, it is durably stored and safe against errors, crashes or any other (software) malfunctions within the database.
SQL / Relational DB
ACID is commonly provided by most classic relational databases like MySQL, Microsoft MS SQL Server (product), Oracle (company) and others. These are known for storing data in spreadsheet-like tables that have their columns and data types strictly defined. The tables can have relationships between each other and the data is queried with SQL (Structured Query Language), which is a standardized language for working with databases - and why these are also commonly called "SQL databases".