Loan - You own the system. The tax credit belongs to you.
Lease - Fixed monthly price for energy generated by a 3rd party system. The tax credit belongs to that 3rd party (owner of the system)
PPA - This is a lease from a 3rd party agreement. You have an agreed-upon price per kWh, per season for production. This will reduce your monthly electric costs, but you will still have a bill due each month to the solar energy provider.