The first is a retainer. Retainer hours come at a significant discount because they might not get used, but are billed regardless.
The second is long-term forward-looking commitment. A monthly rate is at the short side of long-term commitment; a multi-month project feels like a more typical discounted commitment.
You should not discount for daily or weekly commitments. Daily and weekly rates are industry standard. When you offer a discount on a daily rate, you are effectively communicating a willingness to negotiate your underlying rate.
If there's a second strategic decision I want to urge everyone to make, it is "NEVER NEGOTIATE YOUR RATE". With a savvy customer, you will never get any concession on your rate back; once you establish a new floor, that floor is likely to remain there forever. This is the case at big companies and small ones, but be aware that this is such a common dynamic that Fortune 500 companies have people whose performance is evaluated by how effectively they hold the line on bill rates.
If you have to negotiate, negotiate over the total price of the engagement. I know your nerd brain can't separate the total for a project from what the hourly for that project works out to, but they are very much not the same thing.
I am generally of the mind that your rate structure is your rate structure. Clients want to push back on all sorts of stuff. They also want you to sign their master agreements unmolested. Learn to say "no" professionally: to quickly find ways to accomodate your customer's underlying concerns without budging on your price structure.