Direct2D is a hardware-accelerated, immediate-mode, 2-D graphics API that provides high performance and high-quality rendering for 2-D geometry, bitmaps, and text
Direct3D is a high-performance, COM-based API for accessing graphics hardware (GPUs) in a device-independent way on Microsoft platforms.
"If you are willing to limit yourself to vista or later then direct2d would be a little simpler than direct3d"
from question "Native WPF vs. Custom DirectX for displaying large images"
"Direct2d is more or less dead nowadays and one would use direct3d also to render 2d"
from question "2D graphics with C#"
"Direct3d appears in principal to be easier than direct2d but has poor text font handling in the latest version"
from question "2D graph drawing in windows with unmanaged code callable from excel"