The difference is that in the first case you are not setting the Content-Type response header to application/json while in the second this is done.
In first case the response is plain text and looks like this:
"SomeListHere"
And the Content-Type header is set to text/html which is incorrect as this is not HTML. It's text/plain. That's not even a valid JSON string.
In the second case it is a JSON string which looks like this:
{"list":"SomeListHere"}
Also in the first code example you are manually performing the JSON serialization which is plumbing code and should not be done in a controller and should be externalized in a custom ActionResult which is exactly what the creators of the ASP.NET MVC framework have don for you in the face of JsonResult which is your second code example.
Conclusion: if you want to send a JSON serialized representation of some model to the client always use the second approach.