what are the differences between data analysts and data modellers? And also can anybody clarify what exactly is responsibility of Data Analyst?

Data analyst is one who analyzes facts and figures(data) and organizes it in a manner that he is able to project useful information from it. Thus one needs to be strong in algorithms, excel, statistics to be a data analyst.

Data modeler on the other hand is the one who designs the database structure of an application. It requires to understand:
1) Purpose/role of the application in context of business.
2) How users plan to use the application.
3) What kind of information/data is expected from the users by the application.
4) Most importantly to understand the overall workflow in the proposed system.

Def. of Data Analyst is correct and can be understand from vcite, But for Data Modeling you will have understand the business requirement, then decide the Entity, Attributes and Domains , and then build a logical model which you will later convert it into physical model ( Tables ).