Hi Tim,
Click on this link...
http://garden.org/plants/searc...
And it will take you to the page in the Database that shows several different varieties. I'm not familiar enough with the others to be able to give you 'for sure' info.
Don't know about "parsley", I didn't see that one in the database, but 'Snowflake' is there, and it looks like it may be a variegated variety. I think you'll find that they are just different cultivars of the genus Polyscias.
's
So very kind!
Good day! Good gardening!
Tara