"False Oregano"

I have two slightly different plants growing in my yard. Both smell like oregano, and both look like oregano. However, I have been told by a few different people that this is, in fact, "false oregano."
Having spent considerable amounts of time searching the internet for information about these plants, I've come up with nothing.
By the way, I live on the Big Island of Hawaii, where we have a year-round growing season. Sadly, we don't have any soil, so that has to be purchased.

There are many varieties of oregano, and some of them could, in fact, be called "false" because they do not belong to the oregano genus Origanum. Their leaves may have an essential oil profile that resembles oregano, hence the oregano-like smell and taste, but technically speaking, they are not true oreganos. An example is Coleus amboinicus, which we list in our catalogue as "broadleaf thyme"; this plant is widely known also as "cuban oregano" or "puerto rican oregano", yet it doesn't look anything like a real oregano of the Origanum genus. You can see this for yourself in our catalogue: take a look at broadleaf thyme at
www.richters.com/Web_store/web_store.cgi?product=X6478
and compare with a true oregano, greek oregano, at
www.richters.com/Web_store/web_store.cgi?product=X4315
Besides the "false" varieties such as broadleaf thyme, there are Origanum species and varieties that don't have the right flavour and scent, or none at all. A common mistake the horticultural industry makes is to confuse wild oregano, also known as common marjoram. Common marjoram has virtually no scent or flavour to speak of. You can see what it looks like at
www.richters.com/Web_store/web_store.cgi?product=X3890