A Data Warehouse is a type of Data Structure usually housed on a Database. The Data Warehouse refers the the data model and what type of data is stored there - data that is modeled (data model) to server an analytical purpose.
A Database can be classified as any structure that houses data. Traditionally that would be an RDBMS like Oracle, SQL Server, or MySQL. However a Database can also be a NoSQL Database like Apache Cassandra, or an columnar MPP like AWS RedShift.
You see a database is simply a place to store data; a data warehouse is a specific way to store data and serves a specific purpose, which is to serve analytical queries.
OLTP vs OLAP does not tell you the difference between a DW and a Database, both OLTP and OLAP reside on databases. They just store data in a different fashion (different data model methodologies) and serve different purposes (OLTP - record transactions, optimized for updates; OLAP - analyze information, optimized for reads).