Difference Between L/O And Renting?
as the subject say what are some of the differences between L/Os and Renting aside from the owner having the option to buy the property? Second question is can you do a L/O on a HUD property? 
I guess the first question should be "What position are you in?" Are you the one "selling" the lease/option to a Tenant/Buyer? From your question re: HUD, I will assume that you want to purchase a home and then L/O it to a Tenant/Buyer.
1) Can you do it on a HUD property ? Once you buy it, you can do what you please, so long as your lender is ok with it.
2) One advantage to a Lease Option is that the Tenant/Buyer is responsible for the maintenance/insurance/taxes on the place.
On the other hand, if you question was - can I get HUD to lease/option a place to me, the answer is - highly unlikely! They are in the business of selling them outright.