The lens of the eye is equivalent to a convex lens.  It also works according to the theory of the actual image is inverted and minimized when object distance is greater than 2 times of the focal length.  However, eyes to see close objects or distant object are not by changing distance to object or distance to image (because the distance of the lens and the retina are basically the same). It works by the expansion of ciliary muscles to change curvature of the lens to adjust self focal length leading to accurately reflect an image on the retina.  Lighting on the retina is conducted to the brain through the nerves to analyze what the "object" is.

Normally, as human lens gets fiberosis and is gradually hardened after age 40, the elasticity of ciliary muscles can be weakened and leading to the eyeball becomes short.  Also, focus ability of lens is reduced.  The result is to see distant objects clearly, but blurring of near objects. Then the eye condition is called presbyopia.  By the condensation of positive meniscus, wearing reading glasses is supplementary and can make image of the object falls on the retina

Shape

Most magnifiers are bi-convex (such as handheld magnifier, loupe, pendant magnifier, pocket magnifier, keychain magnifier, etc.) or plano-convex (bar magnifier an dome magnifier). But, reading glasses are positive meniscus.

Field of View

As a magnifying glass for reading generally does not need high magnification power, the lens will be relatively large.  So, you can have a larger field of view to facilitate reading.  Nowadays, some of them are even designed to be rectangular to enlarge field of view, and with LED bulbs (LED magnifier, lighted magnifier, or illuminated magnifying glass) so that people can still read in dark environment.  Reading glasses are to be wore on the face and the field of view are 2 small circles, and it only works in bright environment.

Daily Application

Magnifiers are mainly magnifying objects to let people see things and small fonts clearer, not an ideal alternative for vision correction.  Normal people can see tiny things through pocket magnifier, keychain magnifier, pendant magnifier or card sized Fresnel lens.  However, you need to examine your eye by an optometrist before wearing reading glasses since individual eye diopter is different.  So, image of the object will properly fall on retina to reach the intention of seeing things clearly.

Magnifiers and reading glasses belong to convex Lens.  If convert common magnifier to reading glasses, it is equivalent of 1000 - 2000 degrees (equal to 100 times of reciprocal focal length).  Obviously, it’s not suitable for individuals.  Replacing reading glasses by magnifiers in long-term will cause eye soreness, swelling, and headache.  The most serious effect is causing damages to your eyes.  So, you must examine your eyes by a professional optometrist prior to wear reading glasses.  You cannot wear it at will.  Magnifiers are suitable for short-time use and for some special occasions.