If a table is in 3NF it's in 2NF for sure, but not vice versa.
That holds up though at least 5NF. In theory it should also be true of 6NF vs. 7NF as well, but at least the last I heard, it was pretty hard to say much with certainty about 7NF -- including even proving with a given dataset was in 7NF or not, and if not how to transform it to 7NF.
Edit: The specific case of 3NF vs. 2NF:
First of all, you're sort of right that these two aren't as obviously built on top of each other as most of the other normal forms. 2NF deals only with having a composite key (i.e. at least two columns treated as a key for the table) but having an associated field that really applies to only one part of that key. The classical example would be a row consisting of something like "part #, quantity, manufacturer, Division, Division address", where "part #" and "manufacturer" are treated as the key. In this case, the division and division address really apply only to the manufacturer, so to put the data in 2NF, you should separate the data into two tables, one with "part #, quantity, manufacturer" (and "part #" as the key), and another with "manufacturer", "division" and "division address" (with manufacturer as the key). This way, you have only one copy of the data about a part source, regardless of the number of parts you buy from them.
That puts the data into second normal form, but not third normal form. 3NF dictates that each non-key field provides exactly one fact about the key. In the case above, a manufacturer can have multiple divisions, and each division has its own address. Even though the data is in second normal form, the division address is providing a fact about a division, which is a non-key field. To transform the data to 3NF, we have a couple of choices: we might treat manufacturer and division as a composite key, and the address is a fact about that entire key, OR we can separate the address into still another table, so we end up with one table giving the manufacturer and the division, and another with the division and that division's address.