Is farsightedness the same as presbyopia?

Not quite same. Farsightedness, or hyperopia, typically is diagnosed in children, who may end up outgrowing this problem. Occasionally they will need correctsive lenses. Presbyopia is a natural aging process of the lens losing elasticity, that affects almost everyone starting in age 40s. The result is also difficulty focusing on near items; affected patients may need bifocal or reading lenses.
Presbyopia/Farsight. A person who is farsighted can see well far away, but needs glasses to see close-up. This happens at any age. A person who is presbyopic is 40+ and has trouble focusing closeup because the lens and focusing muscles of the eyes are not able to accommodate well-- they lack the ability to adjust to near materials, such as a book or computer screen or smartphone. This is an age-related phenomenon.