Hi Jimi,
I'll take a stab at this. If you see a plant with a Latinized name it's usually a species. By the way, although many people will use "specie" as singular for a species, this is wrong, wrong, WRONG. (When I hear some people saying it, I have to fight a strong urge to slap him/her! LOL I'm kidding--sort of.) Species is correctly used both as a singular and a plural. (Like sheep. You don't say sheeps.)
(There are a few exceptions to a Latinized name being used only for species. I'll deal with them later.) Anyhow, if it's a hybrid, it will either have a non Latin name (English, French, Chinese, whatever), or it will have two (sometimes more) Latin names with an X (or x) between them, signifying a cross between those species. (Or between two or more hybrids, just to make it more confusing!)
If someone makes a cross, they can register it with the Royal Horticultural Society and name it. From that point on, all crosses made from the same parental types are known by that registered name. In the example you used, any cross between sanderianum & philippinense is Michael Koopowitz. There are some crosses that never get registered and must always be identified by the parental names with the x between them. I have no idea why some don't get registered.
The Royal Horticultural Society has a website where you can look up crosses. You can inquire what the proper name of the offspring of any cross is, or you can type in the name of hybrid and it will tell you the name of the parents. The URL is:
http://www.rhs.org.uk/plants/registerpages/orchidresults.asp
This information can also be found by software like OrchidWiz. In my opinion, it's
much easier to use than the RHS website, which is rather cumbersome.
There are some very old hybrids that may have Latinized names. One I can think of off the top of my head is Phragmipedium Sedenii, a cross between schlimii & longifolium. Originally, hybrids could have Latin names, then the powers that be ruled against it. I believe natural hybrids are still allowed to be given Latin names.
The last part of a name is a clonal name, and they are always enclosed by single quotation marks. In your example, 'Birchwood' & 'Fox Croft" were particular clones of presumably superior examples of philippinense & sanderianum, respectively. All Paph philippinense 'Birchwood' originated as a single plant, of which divisions have been made.
So, I've probably made this as clear as mud! I can only say that you will find the terminology easier to use, and you'll feel more comfortable with it, as you continue to work at it. It will get better--I promise!
If there are any items I've missed, I hope others will jump in.