Safeway here was clearing out two spice lines, The Spice Hunter and Morton Bassett/San Francisco. I ended up buying close to $100 worth, I had five bottles labeled oregano, two from one company, three from the other. When I opened them all up to put into the appropriate larger containers I have here for both kinds of oregano, they all smelled like my Mexican stuff. It's more pungent than the Greek, with a sharper nose on it. Not only is Greek lighter, but it also has a heavy citrus flavor and the finish doesn't linger nearly as long as the Mexican. Both of these companies are out of California, one SF, the other SLO. Indo European brand which has the Greek I buy, is out of Glendale, CA.
I had my sister when she was here recently whiff both of these, as she didn't know the difference between the two. She never knew there were two kinds, and I've run into this before with management at grocery stores in the past when I've asked what kind the bulk they sell is. They tell me they thought there was just 'oregano'.
I now can tell from the aroma which is which, and just to be sure, if it isn't labeled one way or the other, if you know the source, I can only suggest you find out by inquiring with the company. My Italian food certainly tastes better using Greek rather than Mexican, but I used Mexican for years before I even knew the difference.
If you order yours from mail order spice companies or are lucky enough to have their shops near you, they specifically label both kinds. This is truly the only way you will know, unless you can tell the difference by smell or taste. I just did a taste test of my two, and the flavors are distinctly different.
There is California basil and French basil, those flavors are also distinctly different. Each color of peppercorn is different, as is each different 'chile' pepper. I personally cannot buy anything labeled chile or chili powder, I only buy the specific chile in powdered form.
The Spice Hunter and Morton Bassett are definitely a Mexican oregano with the labeling 'Oregano'. If your oregano isn't heavily citrusy and light, it most probably is Mexican. The label, like Spice Hunter's, that denotes the spice is good in Mediterranean or Italian cooking doesn't necessarily mean that the oregano is Greek.