I graduated at the top of my/the class
I graduated first in my class
I graduate with honors
I graduated cum laude
I found the above expressions on google, but I'm not sure whether they mean the same thing. If not, what are the differences? Are some of them more formal than others? Or used in British rather than American English?
They are all potentially different. "Honors", including—but certainly not limited to—Latin honors such as cum laude, magna cum laude, and summa cum laude, is something that one's institution confers on one. Other types of honors include the hono(u)rs degree.
"First in my class" means that one ranked first in terms of some metric (e.g., grade point average). One's institution may or may not specifically honor this achievement; if they do, it may be valedictory in form.
"Top of my class" is much more vague and could mean almost anything.
It's sometimes possible to generalize what a certain term means in British or American English; see the British undergraduate degree classification, for example. In other cases, it's most useful to look at the definitions used by the institution of interest. For example, every year the United States Military Academy, commonly known as West Point, specifically recognizes the graduate with the highest class rank, which is only partially based on academic performance.
Generally speaking, regardless of how good your grades are, you should not use the terms "with honors", "cum laude", "magna cum laude" or "summa cum laude", unless these honors have been conferred on you by the institution from which you graduated. Where such honors have been conferred, they will almost always be inscribed on your diploma, and they will also be recorded on your academic record.
If you graduated with higher grades than any other student, but were not awarded any of these honors, or if you attended an institution that does not award such honors, you can certainly say that you graduated first in your class; you would be foolish not to. I would not personally use the phrase "top of my class" unless I was referring to my performance in my final year at a secondary school.
Finally, the honors system summarised above, usually called Latin Honors, is most commonly used in the USA. It is also used in some overseas countries. The UK, and most Commonwealth countries, have different ways of awarding honors.
British and American usage are very different. Expressions like "cum laude" are not used.
In Britain, as a result of "grade inflation" nearly all bachelor degrees are "honours degrees", with the class of the degree being 1st (the best), 2:1, 2:2, and 3rd (the lowest honours class)
Some universities have their own ways of describing particularly succesful students. In Cambridge, the mathematics student who gets the highest mark in the final exam is known as the "senior wrangler" (while the lowest 3rd class degree was awarded a wooden spoon).
If you want to describe your own degree you can't use British descriptions, unless you come from a country which uses the same classification. You can't say "I got a 2:1 from Harvard" because American Universities don't classify degrees in the same way. Instead, you use the native description, supplemented by an explanation in English.
I graduated with distinction, which put me in the top 10% of my class.
At university I was placed first out of my class of 150 students.
