onclick = "a()"
This is done while writing in designer form page like *.ASPX or *.ASCX, i.e. while writing in client side.
Similar approach can be used for defining click via script language like in Javascript or so.
onclick="JavaScript:a()"
This is done while writing in code-behind files. They reside on server and needs to know that the execution of method a() is client side and defined in scripts.