What is the difference between the various Rasterize options?

To simplify what JJMack stated:

Rasterize type layer - turns type to pixels, can no longer edit with type tool

Rasterize layer - removes what was special about it - like a smart object. No longer a smart object, just a regular pixel layer

Rasterize layer style - can no longer edit the style, it becomes part of the layer - so a drop shadow is now pixels in the layer instead of an effect.

You rasterize none Raster Pixels when you want to use some feature that requires a normal Raster layer.

Text layers are vector graphic layers. That what text is.

Shape Layers are more or less a fill layer (solid color, pattern, or gradient) and Smart Object  Layers transform like Raster Layers however the late pixels are not changed the are set in concrete they can not be changed by Photoshop Tools or filters.

So if you need to modify smart object layers pixels you have to rasterize the smart object layer.   I do not believe there is any difference between Rasterize Type and Rasterize Layer, the Layer content will be replaced with a normal Raster pixel layer.

It is the Layer type that determines which of the option is in the right click menu.  The layers composite view, like Smart filters  and the associated layer transforms, would be applied to the smart object layers pixels.

Layer Style pixels are not Part of the layer content there are pixels rendered to add visual effects to the layer composite view.   If you use Rasterize Layer, the layer style will remain intact, attached to the Normals Raster layer.   If you use Rasterize Layer Style, the layer style pixels will be rendered for the layers content and applied to the normals raster layer and the layer will not  have a layer style attached to the layer.

So the only difference is weather the Normal Raster Layer will or will not have a layers style attached.

The menu Layer>Rasterize>Which Type  spells our the layer kinf toe be rasterize more.