Wide ruled (or Legal ruled) paper has 11/32" (8.7mm) spacing between horizontal lines, with a vertical margin drawn about 1-1/4" (31.75mm) from the left-hand edge of the page. It is commonly used by American children in grade school, as well as by those with larger handwriting.
Medium ruled (or College ruled) paper has 9/32" (7.1mm) spacing between horizontal lines, with a vertical margin drawn about 1-1/4" (31.75mm) from the left-hand edge of the page. Its use is very common in the United States.
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The only real difference between wide ruled notebook paper and college ruled paper is the height of the blue lines. In grammar and high school, students may only be allowed to use one or the other. Some schools and some teachers are very strict about their school supplies and will only allow a wide rule notebook, or only loose leaf college rule paper.
Wide rule is better for people with handwriting that is larger and also for those with handwriting that is less than perfect. Writing, whether it is hard to read or not, will not be improved by being cramped onto smaller lines. The wider spaces also mean that there are fewer lines per page. If you are in high school and you find composition difficult, this is good news for you, since it will take less writing to fill up a page, and most teachers below college level put a page rather than a word requirement on essays and other writing assignments.
College rule paper is ideal for those who have small handwriting in the first place. Tiny letters look better on smaller lines, as well as being easier to read on smaller lines. It is also a better choice for students who enjoy writing assignments and those who tend to get wordy in their compositions*. It gives a writer more space to hash out ideas. Parents will need to buy paper less often, too, simply because less paper needs to be wasted on first drafts, since there is more available room on each page.
Outlines, which are required in most junior high and high school English courses at some point, has pro and con arguments associated with either type of paper. On the one hand, there is more room for a multi-topic outline on sheets of college rule notebook paper. However, since the point of an outline is to lay things out in a simple to read style, the taller lines of the wide rule sheets may make an outline look better and make it easier to read.
Likewise, an argument could be made for both types of paper when it comes to note-taking. You can certainly get more notes into college ruled notebooks, but those on wide rule paper may be easier to read quickly.
*This used to also come in handy outside of school, when writing notes and letters, but this is only still relevant if there is any child over the age of 8 who still communicates with pen and paper instead of a cell phone.