They both do essentially the same job, with the exception that you can specify a particular frame to draw with DrawImage if you use LoadAnimImage.
As a general rule, use LoadImage for a single image, and use LoadAnimImage for a single image that is made up of multiple frames (like different states of a character running, for example). You would then be able to call DrawImage with a frame of 0, then 1, then 2, then 3 (for a 4-frame image) to simulate your character running. Alternatively, you could use LoadImage 4 times, then call DrawImage 4 times, but LoadAnimImage works better in loops and such (for the programmer).
Did I thoroughly confuse you with my dodgy explanation? =)
As a general rule, use LoadImage for a single image, and use LoadAnimImage for a single image that is made up of multiple frames (like different states of a character running, for example). You would then be able to call DrawImage with a frame of 0, then 1, then 2, then 3 (for a 4-frame image) to simulate your character running. Alternatively, you could use LoadImage 4 times, then call DrawImage 4 times, but LoadAnimImage works better in loops and such (for the programmer).
Did I thoroughly confuse you with my dodgy explanation? =)