First of all, note that the question about "difference" makes no sense, as it usually happens with this uncertain concept. What would it supposed to mean? Instead of asking about "difference", you just need to understand how things work.
If I could take your question literally, from its title and body, I would have to ignored the question tags because, strictly speaking, they are not directly related to HTML, and the question is HTML. Then the answer would be: in HTML, there are not drop-down boxes or list boxes. There is one HTML element which play such roles, depending on some options:
<select>
element:
https://www.w3.org/wiki/HTML/Elements/select[
^].
As to the classes named
ListBox
or
DropDownList
, they are just the wrappers using this HTML document. When you use such classes, the ASP.NET HTTP response generates HTML with
<select>
element. In particular, in "System.Web.Mvc", this is based on the class
System.Web.Mvc.Html.SelectExtensions
which provides a way to render different forms of this elements using appropriate static method (something like
factory methods):
https://msdn.microsoft.com/en-us/library/system.web.mvc.html.selectextensions%28v=vs.118%29.aspx[
^].
There are similar classes in the assembly "System.Web":
https://msdn.microsoft.com/en-us/library/system.web.ui.webcontrols.listcontrol%28v=vs.110%29.aspx[
^].
—SA