A Database is basically a structured collection of data or records which are stored in a computer system. This structure is gained by proper organization of data through the database model.
On the other hand, the word Schema itself stands for shape or plan. Thus this word is mostly used for models or diagrams or formal logic. As far as databases are concerned, Database Schema is the structure that is described in the programming language and is supported by database management systems.
Thus Schema is the graphical depiction of the structure of the database system. And database itself is the structured collection of data.