There's quite a few differences between the two, and many other types of headmates besides just tulpas and soulbonds.
As Addy said, tulpas are intentionally created. They are developed over the course of months or years with the intention of them becoming separate and independent. The vast majority of tulpamancers I've encountered believe their tulpas are psychological in nature rather than spiritual - they're a fragment of the original that is nurtured and developed over time. Often they start off resembling children, and like all people they usually mature with age.
Soulbonds are spiritual in nature. They often show up randomly, but some systems can also invite them; from what I know, they are always fully formed when they arrive. I think one of the more common beliefs regarding them is that they are living their own life in another universe, and develop a connection with the host here through spiritual means. Via that connection they can interact with the host, and sometimes front. Most soulbonds seem to come from "fictional" sources, but not all.
But like I said, there's many types of headmate besides just these two! For example, fictives resemble soulbonds in that they originate from fictional media, but are generally seen as psychological rather than spiritual. Because of that, there tends to be a little more room for crossover between fictives and tulpas (whereas the potential for a mix between a soulbond and tulpa is practically nil). ^^