Question

how does alluvial fan differ from a delta?

Answer 1

alluvial fan: " usually created as flowing water interacts with mountains, hills, or the steep walls of canyons. Streams carrying alluvium can be trickles of rainwater, a fast-moving creek, a powerful river, or even runoff from agriculture or industry. As a stream flows down a hill, it picks up sand and other particles—alluvium. "

~source: http://education.nationalgeographic.com/education/encyclopedia/alluvial-fan/?ar_a=1

in short can be found at the base of the mountains, here's a pic:

Answer 2

next is delta fan: " are wetlands that form as rivers empty their water and sediment into another body of water, such as an ocean, lake, or another river."

source: http://education.nationalgeographic.com/education/encyclopedia/delta/?ar_a=1

in short , imagine rivers from a land that will merge into a big ocean/sea etc.
sample pic for further understanding: