Software design is the stage that comes next after freezing software requirements. The requirement specifications are given to the team of developers headed usually by a project manager. The project manager or the technical lead decides on the software architecture, OS, front end, back end, database etc. System design or ERD (entity relationship diagram) is prepared once the initial database design is clear with the table structures to be built in the database.
Software design is nothing but the conceptual design of the database, tables and table structures, relationship of various fields of tables with one another. Once conceptualized, it is discussed among the team, make any changes if required and then freeze it. Once the concept is finalized, the database is designed by creating tables and building relationships. The next phase that comes after is the coding.