drainpipe

As nouns the difference between eaves and drainpipe

is that eaves is the underside of a roof that extends beyond the external walls of a building while drainpipe is a pipe connecting the drain to the gutter.

As nouns the difference between drainpipe and downpipe

is that drainpipe is a pipe connecting the drain to the gutter while downpipe is the drainpipe that connects a roof-line gutter with the ground.