There are many different styles of collars, lace, peter pan, sailor, bow, etc. Forever21 even has clip on collars, I've seen a peter pan blue sequins one there.
Lace - Typically white or cream colored, any lace pattern, can be tied on to neck, some shirts have lace collars built in, but you can get a loose one to add to any shirt.
Peter Pan - A rounded edge, any color (traditionally; white), close to neck. It is elegant and cute!
Sailor - Tied in the front with a square shaped piece of material on the back. Can be added to any shirt or bought already on the shirt.
Bow - A floppy bow collar that lays gently on the chest, perfect for a dressy night out and also a casual day.
Jabot - Multiple layers of fabric or lace slighty scrunched, long or short. This was traditionally on male clothing in the "old days" on sailors, you can see on Pirates of the Caribbean. Now favored in women's fashion, and modern versions may vary.
Shawl - Seen most on tunics and warm jackets and sometimes on blazers and cardigans. A relaxed and simple collar that is elongated with rounded edges, like a stretched out peter pan collar, but it can be smaller and shorter.