I'm pretty sure you can't change this after you make the callout. You have to change the type before you draw the callout. A note about Detail Callouts though, you can't put an elevation marker in them, so make sure you won't need to do that.

That's annoying.
What would one use a plan view for anyways? Stairs?

When working with the default Revit tempaltes and creating a Detail callout (depending upon the view you are creating it in) a number of different "Types" are available in the Type Selector. If you are starting in a floor plan view, then the two types available are the "Floor PLan" and "Detail" types. If you start in a section view, there are three types available: "Building Section", "Wall Section", and "Detail". If you are starting in an Elevation, three types are available: "Building Elevation", "Interior Elevation", and "Detail". The only difference between all of these different types is where the view is saved inthe Project Browser. The "Detail" types get saved in the Detail Views category whether it was created in a floor plan, section, or elevation view. The other types such as Floor Plan are saved to their appropriate locations, in this case the Floor Plans category.

You can select the Callout object and change its type through the Type selector, and all this does is move the view from one category to the other.

Ron is not exactly correct. There are differences...as I found out just the other day. Doing callouts for plan details - problem is I'm cutting the view in a wierd spot that doesn't really show up in any of my plans in my set so I'm cutting them in my working view and referencing other view in my set...anyway, I accidentally used Detail Callout instead of Floor Plan - you have no control over the view range anymore. If I change the view range of my working view, it adjusts the view range of the callout. Unless I change the callout to no longer have a parent (which is an option) the view range changes with my working view. Once you get rid of the parent, you can't change the cut plane of the callout, just the view depth. If I use Floor Plan instead, I can change the view range as I would normally like to in a floor plan. I try NOT to use the Detail type at all, every time I do I find something else that frustrates me about it.

And once you've created it as a Detail view you CANNOT change it to something else. You have to recut the view.

90% of the time I don't see why people use detail over plan. If you cut a plan you can still use plan regions, change your crop, and do other things. If you cut a detail you are restricted to having exactly what the original plan has. I personally hate using detail views most of the time because of its limitations. This is the same thing when using the section tool...I cut sections not details generally.

Horizontal detailing for instance.
And the "standard" type is selected by Revit in compliance with the view you're in. In Plan Views, you'll get a Plan Detail. In Section you'll get a Callout.
Why? I really have no idea... someone once thought this would be a nice feature I guess... Personally, I don't use them. I just duplicate the Plan View or use a Section. When used as a Detail view, I'll change my Project Browser sorting parameters to Detail instead of Plan/Section.
I do have different types of Sections defined btw, but you can switch between those as you please.