How can I use the "Publish" function in Visual Studio 2008 without erasing the contents of the target folder?
John is right, the only difference is one of your projects is a Web Site Project and the other is a Web Application project. You will not see the "convert to web application" option unless you are in a Web Application project. I know... it is very misleading. The reason behind this stems from the the way you convert to a web application project. If you plan on converting it(which can be a real pain in arse, depending on how it is set up) then you need to be aware of a few differences:
In a Web Application project everything is pre-compiled all the codebehind pages will be compiled into a .dll ---- In a Web Site Project nothing in the project is pre-compiled, the compiler will compile everything to ensure it is valid but none of the compiled pages are uploaded. When a user first attempts to access the site each page is compiled into its own dll. This means in a Web Site Project you are able to upload a single codebehind file.
Namespaces - In a Web Application project namespaces are created by default in a Web Site Project they are not. So you may have to spend some time adding them if you plan on converting them.
Project files - you will notice that A Website Project does not have a "cproj" file a Web Application project does.
I have converted a few of these project I find they go fairly smooth as long as there is not a lot of code in the "app_code" folder. You can give it a try and see how easy it is, if it looks like it is going to be a pain, I would suggest FileZilla just FTP it and save yourself some headache.
Good Luck
That dialog is different for Web site projects and Web application projects. In my MVC projects (Web application projects), I see the additional options. In my regular ol' web site projects, I see the first dialog posted.
Not sure if this option will be suitable for you but you could use the copy website function from the solution explorer. Click on the "Copy Website" icon at the top of the solution explorer.