Spherical and Astigmatism Components of a Prescription.
This refers to the shape of the optical system used to model the eye. So, a spherical prescription represents an optical system (that bends the incoming light) as if it’s passing through sphere or football.
In astigmatism light passes through the optical system represented by a shape like an oval or rugby ball. The number in the prescription box representing astigmatism, called the CYL (short for cylinder) can be written in a plus form or minus form e.g. CYL +1.50 or CYL -1.75
Normal Focus

Long Sightedness

Short Sightedness

When the images is focussed on the retina, it is the sharpest it can be. In long sightedness the iamges focus beyond the retina and so it is blurred. In short sight the image focus infromt of the retina and so it is blured.
In astigmatism light passes through the optical system represented by a shape like an oval or rugby ball. The number in the prescription box representing astigmatism, called the CYL (short for cylinder) can be written in a plus form or minus form e.g. CYL +1.50 or CYL -1.75
Plus lens corrects long sight e.g +2.00

Minus lens correct long sight e.g -2.00

Presbyopia.
Is represented by the eyes inability to focus on near tasks such as reading due to hardening of the lens inside the eye. Here where need an additional focussing power prescribed as reading glasses.
It is represented in the prescription as the ADD or the Near Prescription. Such patients there a number representing the distance vision glasses hence distance glasses.
Then there is the near part of the prescription representing the reading glasses. Sometimes there can be an intermediate part too, called the Intermediate Add or INT ADD. This is specific for a viewing distance required solely for computer use.
These prescriptions for reading or computer are either written in short form as the Near Add or the Intermediate Add or alternatively, they can be written in full form in terms of the actual prescription. It doesn’t matter it just different conventions of writing the same thing