How Database design is different from Data modeling?

Database Design
The process of designing a database is known as database design. The database design generates a complete data model of the database as an output. Database design, strictly speaking, refers to the comprehensive logical model of a database, but it may also refer to physical design decisions and storage characteristics.

Data Modeling
It may be thought of as the initial step toward database design. Data modeling is the process of constructing a conceptual model based on the relationships between different data models. Moving from the conceptual stage through the logical model to the physical schema is part of the process. It entails a methodical approach to data modeling approaches.