They are both Barber Hones. I don't know for sure (newbie, someone else needs to step in here and give you more info) but my Swaty seems to be a finer grit than the lithide. It also seems to bring out a better edge, but that could be my technique (or lack of). Until I got the Swaty I used the Lithide for a finishing hone which is what Tilly described it as (came in her beginners kit).
Hope this helps there are a lot of choices in hones. For example, today I found out there is a stone you can use instead of a strop. Forgot the name of it, I was on the cell phone in a hardware store.
This is a bad picture they are lighter brown than this
http://i1.ebayimg.com/01/i/07/a1/ee/69_1.JPG