Difference between "size" and "magnitude"

Solution 1:

Usually, size connotes physical dimensions while magnitude connotes either a numerical measure (particularly a non-linear one) of any sort of amount or metaphorical size.

"What size is that screw?" (Physical dimensions)

"A problem of immense magnitude" (Metaphorical size)

You can also use size to mean metaphorical size, but you usually can't use magnitude alone to mean physical size. (Nobody would say "What's your sneaker magnitude?")

Solution 2:

The difference/usage exists mainly in natural sciences (physics)

• size: has nearly always a linear scale, if the size gets bigger, it also means higher positive absolute values of the according physical quantitiy (temperature, volume,...)
• magnitude: has more the meaning "order of magnitude" and is often used esp. for logarithmic scales when linear scales are too unhandy and typical order of magnitudes like milli, nano, ... fail for practical use (e.g. magnitude of earthquakes, apparent magnitude in astronomy (here the unity is mag but a more negative mag value means a brighter astronomical object! so its counter intuitive to typical physical quantities.)).

Solution 3:

"Magnitude" connotes the quality of being big, whereas "size" is merely a measure of how big something is.