The exact classification of early american periodicals is often confusing. A periodical is, by definition, issued at intervals. Therefore, a daily newspaper is not a periodical. In 18th century America, there were no daily publications, making each and every magazine and newpaper a periodical.
What is a magazine? Literally it is a storehouse of information- taken from the same root and definition as the magazine of a ship, used as a storehouse of munitions. The word "magazine" was first used in the context of a periodical in 1731, in London, England, by Edward Cave (aka Sylvanus Urban) for Gentleman's Magazine. Clearly there were prior publications of similar content, periodicity and scope which did not have the name "magazine". So semantically, Gentleman's Magazine was the first magazine to actually be called a magazine, though not the one which first utilized the format.
What is a newspaper? Indeed, news periodicals date back to Roman times. News periodicals contain factual accounts of events. The first english language newspaper is considered to be The Oxford Gazette, first published in 1665. In America, the first newspaper was Publick Occurrences, printed in 1690 and banned after one issue (therefore technically never being a periodical). The Boston News-letter, begun in 1704 was the first successful American Newspaper.
The first American magazine is presently considered to be Willam Bradford's American Magazine, first published in January 1741 (beating Benjamin Franklin's General Magazine to the press by a few days) closely following the format of its british forerunner, Gentlemen's Magazine.
Now comes the conundrum. Early magazines and newspapers all published periodically. Many magazines contained news and many newspapers contained essays, literature as well general non-news content.
For instance, examining John Peter Zenger's New York Weekly Journal, classified as a newspaper and published in 1733 in comparison to William Livingston's Independent Reflector, considered to be a magazine, published in 1752, one would be hard pressed to discern a difference in content. There are many other examples of comparable but differently classsified periodicals published throughout the 18th and 19th centuries.
Size and paper type can't be used as strict criteria, since some publications presently recognized as magazines were printed on newsprint and both newspapers and magazines come in all different sizes.
In the 21st century, most readers pretty much know which is which (of course, The New York Times includes its own magazine!!), but for a considerable amount of time in the past, the waters were considerably muddier.