Not a different "license" but a different "type rating" - a subtle, but important, distinction.
Although a 747 and a 787 have the same basic controls, controlling them through all phases of flight, with full understanding of the limitations, procedures, and emergency actions differ enough that specific training is required for each
When an aircraft becomes "suitably complex" (decided by the licensing authority) then a separate "type rating" is required
In many countries, there is a Class Rating that covers many different Types. In my (Australian) experience, newly licensed pilots are officially allowed to fly any aircraft having a single piston engine and maximum take-off weight less than 5700kg (12,500lb), with fixed pitch propeller, and fixed undercarriage with nose-wheel steering.
With further experience and testing, a pilot may have the fixed-pitch or fixed-undercarriage restrictions removed.
Once you want to fly a multi-engine aircraft, a turbojet, or a bigger plane, you'll typically need a specific rating for that exact aircraft.
There can be exceptions. For example, there was an aircraft with twin centre-line thrust piston engines that I was allowed to fly without a specific type rating. The most challenging part of flying a twin-engined aircraft is dealing with the off-centre thrust if one engine fails. If both engines are centreline-thrust (one at the front, and a "pusher" at the rear), then there is not such a challenging asymmetric situation when one fails.
The specific regulations (e.g. Australian tend to be quite wordy.
You will need a different rating, if the aircraft in question or different categories in classes. A person who holds a pilot certificate with a airplane single engine land rating, for instance, may not serve as PIC in a rotorcraft helicopter without a rotorcraft helicopter rating added to their pilot certificate, or received additional type specific training and signoffs per §61.31(h). These are US regulations but ICAO has similar ones as well. In addition for large aircraft, you will need to be type rated on the individual aircraft in question in order to operate them as PIC or serve as a required pilot flight crewmember. You are also required to requalify every 12 months on type ratings in order to operate said aircraft.
So to your original question, a person who has a current type rated for required pilot flight crewmember duties on a Boeing 747 cannot perform the same duties on a Boeing 787, 737, etc. without being type rated on those aircraft as well.