Home & Business is the highest level, it contains everything in the personal versions of TurboTax.   It does not prepare business returns such as for LLC, C Corp. or an S Corp. For that you need TurboTax Business which only comes for a PC.

Actually all the Desktop programs have all the same forms so you could use a lower version, even Deluxe.  You just get more help in the higher versions.  The Desktop Home & Business program would be the same as the Online Self Employed version .  Just a different name.  But the Desktop programs have many advantages over the online versions.  Like you can see and enter into the actual forms and do more than 1 return.