A BI Analyst is a person who works with BI tools to perform analysis. Generally speaking they would be a person who is somewhat educated on data warehousing and understands how a star schema is modeled.
This allows them to do things such as perform ad-hoc analysis either through a reporting tool or using SQL to create the charts, graphs, excel sheets, etc. that the business users require.
They can also serve as the middleman between business and IT when creating new BI functionality. Basically will work more with the technology and business users as opposed to trying to play that single role.
It is not required of you to specialize in MS SQL/Oracle to go in data analyst / Business Intelligence.