I think you should read this first:
http://en.wikipedia.org/wiki/ASP.NET
http://en.wikipedia.org/wiki/Visual_Basic.net
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In my opinion: ASp.net is mainly for web development and webservers ( if you're interested in web development and learning how to create websites and that stuff go for ASP), but visual basic is more concentrated on programing (i.e: creating programs, web browsers, and other applications).
i never used ASP.net, but i used VB.net before in creating some programs, it's kinda fun if you like programming.
But i'm no expert, i'm just trying to help.
http://en.wikipedia.org/wiki/ASP.NET
http://en.wikipedia.org/wiki/Visual_Basic.net
.............................................................
In my opinion: ASp.net is mainly for web development and webservers ( if you're interested in web development and learning how to create websites and that stuff go for ASP), but visual basic is more concentrated on programing (i.e: creating programs, web browsers, and other applications).
i never used ASP.net, but i used VB.net before in creating some programs, it's kinda fun if you like programming.
But i'm no expert, i'm just trying to help.