In projection paint mode, you're painting on a transparent layer on top of the model. If you click the 'Apply Projection Paint' button, this layer ('the projection canvas') is projected onto the model.
This mode allows you to paint over seams and ignore the distortion caused by the UV mapping.
The projection view, the reference layer and the projection canvas can be exported and imported, allowing you to continue the painting at a different time or edit the projection canvas in an external paint program.
In 3D paint mode, you're painting directly on the decals of the model.
If you open a UV viewer, you can directly paint on the textures in 2D mode with the splines of the model as a reference.