Can someone tell me the difference on a 1861 2 1/2 dollar gold coin the type 1 and type 11 and a business strike. Thanks

The Type II reverse is Longacre's modification. In particular the arrowheads are noticably thinner and the arrow shafts a bit longer. In fact, all the devices have been lightened a bit - letters, numbers, eagle, etc.

Just go up on eBay and look at the pre-1859 and post 1860 Philly's (SF had a lot of left-over dies), you'll see it. It's easiest to tell on the $10.

BTW, from the wording of you question I would take it that you're looking at the Breen Encyclopedia. If so, please be aware that as a friend once said: "Rare is the third most common word therein."