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?")
Both arise and rise are irregular verbs.
When an opportunity, problem, or new state of affairs arises, it begins to exist. This is the most common meaning of arise.
He promised to help Rufus if the occasion arose.
A serious problem has arisen.
The feeling of hope arose from the people.
When something rises, it moves upwards.
The sun rises in the morning.
Clouds of birds rose from the tree-tops.
When someone who is sitting rises, they stand up. You can also use rise to say that someone gets out of bed in the morning.
Cambridge Dictionary also lists rise for "to begin to oppose or fight a bad government or ruler":
The people rose (up) against the oppressor/tyrant/dictator.
Please visit here to see other meanings listed for rise which all are connected with moving upward.
See Here.
Best Answer
You can find both words in most of dictionaries. As a physicist I would not use the word "dimension" in a daily life. For me, this is a mathematical term designated to a property of space. The noun "size" refers to geometrical properties of objects that surrounds us. Below are some daily meanings of the noun "dimension" from dictionary.com.