PubMed vs. MEDLINE
It's kind of a trick question...
PubMed is a database service—a way to interface with the raw data—provided by the National Library of Medicine (NLM). The database that PubMed provides access to is called MEDLINE, also created by the NLM.*
In addition to PubMed, you can also access MEDLINE through an EBSCO interface and an ISI interface. All of them access the same database (MEDLINE), but each has different capabilities and will provide a different user experience.
In other words, PubMed is one way to access MEDLINE.
Which one should I use?
It's really just a question of preference. PubMed is more user-friendly, but EBSCO and ISI give you more control over your searches (EBSCO also offers an optional graphic display of your results.) Any of them will work just fine, and we do have access to tutorials on all three.
*If you want to be geeky about it, PubMed actually accesses a few citations that aren't in MEDLINE—about 2% more. If you want to be really geeky about it, here are the details: MEDLINE, PubMed, and PMC (PubMed Central): How are they different?