Two of the largest available savings come from books most students are nervous about buying. Here is what is actually true.
International editions
These are printings produced for markets outside the United States, typically softcover, sometimes on lighter paper, and often a fraction of the US price. They are legal to buy, own and resell in the United States — the Supreme Court settled the question of importing legitimately produced foreign copies in Kirtsaeng v. John Wiley & Sons (2013).
The content is usually identical or near-identical. What can differ: problem sets at chapter ends, figure numbering, occasionally units or example data, and page numbers. If your homework is assigned as "problems 12–20 on page 340," that difference matters. If it is assigned by topic, it usually does not.
Older editions
A textbook's price falls dramatically once its successor ships, frequently by an order of magnitude, while the underlying material — especially in mathematics, physics, and introductory sciences — changes very little between consecutive editions. Publishers reorder chapters and refresh examples; the calculus does not move.
The exceptions worth respecting: fields where currency genuinely matters, such as law, accounting standards, clinical medicine, and anything tied to changing regulations or technology. In those, use the assigned edition.
How to check before committing
Ask the professor — this takes one email and is the only definitive answer. Failing that, compare the tables of contents of both editions, which are often visible in retailer listings, and find a classmate with the current edition to spot-check the problem numbering for the first assignment.
The one thing that will actually bite you
Access codes. If the course requires an online homework platform, no older or international edition solves that, because codes are single-use and tied to the current edition. Check for a code requirement first; it determines everything else about how you buy.