The photo you provided is actually a great example showing the differences when viewed from the top. Haddoni are typically smoother looking, lie flat, and have short tentacles that often look like little spheres that are evenly spaced. Gigs have more of a ragged appearance, are typically more folded, have shaggier tentacles that -- while they are arranged in rows -- don't appear as evenly spaced. Keep in mind that there are times when sick or acclimated gigs look at lot like haddoni. However, it's extremely rare for a haddoni to look like a gig. The area around the mouth -- often referred to as the "lipstick" can be red, green, yellow, and other colors. However, it's up to debate if gigs ever have red lipstick, while it's common for haddoni.
If it were a video, you may see a gig's tentacles appear to be vibrating. It's not a tell-tale sign, since haddoni are known to do it as well, but it's they oftentimes don't have long tentacles, it's easier to see with a gig.
If you were to look at the underside of the nem, gigs have colored verrucae (spots) which are typically blue or purple. Sometimes they are very visible, other times not so much. Lately we've seen a lot of carpet nems with orangish-brown verrucae and these nems are S. helianthus, which are not hosting nems that may actually eat clowns. The stalk/stem of haddoni are relatively thick, while gigs are narrow.
I hope that helps!
