Are these three all the same thing being inconsistently named by different manufacturers?
100BASE-FX WDM uses separate wavelengths (1310 nm & 1550 nm) for Tx & Rx over a single strand of fiber. I cannot find any documentation for 100BASE-FX that mentions using WDM over a single strand of fiber. Standard 100BASE-FX uses 1310 nm over two separate strands for Tx & Rx. This leads me to believe that this is 100BASE-BX being incorrectly called 100BASE-FX WDM.
100BASE-BX uses separate wavelengths (1310 nm & 1550 nm) for Tx & Rx over a single strand of fiber.
100BASE-BX10 apparently works the same way as 100BASE-BX but I can't find any differences or whether they're compatible.
Further to my comment, I think you're right about them being overlapping terms - mis-used in various ways.
You can download the actual IEEE 802.3-2012 standard here... it's interesting reading if you're in the right frame of mind.
The relevant part of the standard is Section 5, Clause 58, which starts with:
... and goes on for 34 pages, and it always refers to the standard as 100BASE-BX10, never just -BX. And out of the whole 844 pages that make up Section 5, WDM is used only 3 times (in one of the 10Gbit over fiber standards).
So I'm sure you're right that they're all the same thing. (And if it were me, I'd now annoy anyone who asks by insisting that the real name is 100BASE-BX10 and anything else is sloppy terminology.)