How Can I Differentiate Login Of Agent And User By Clicking 'Login' Button?

If this is web forms then give each button its own click event and you'll know which was clicked by the event that is fired. If mvc then look at the Request.Form["XYZ"] where XYZ is the name of the respective buttons, and the one that isn't empty is the one that was clicked

<input type="submit" name="LoginAgent" value="Login"/>
<input type="submit" name="LoginUser" value="Login"/>

// in your code

if (!string.IsNullorWhiteSpace(Request.Form["LoginAgent"]))
{
    // agent login clicked
}

You can also use the above technique with webforms if you don't want to use click events.

Edit: sorry, above is in c# and not vb.net but you get the gist, it's easy to convert it

thank you F-ES Sitecore and Peter Leow