With no official confirmation of either title, "HL3" has come to refer to whatever is next in the series. I've seen tons of comments across different sites that continue to "correct" this but I really don't think it is a distinction that needs to be made.
The distinction is absolutely significant. It's all about expectations. The originally promised "HL2:Episode 3" didn't need to be some huge revolutionary product, just a satisfying conclusion to HL2 and its episodes, while setting up the scene for the next game. As soon as people start saying "HL3" they expect some grandiose, ground breaking product.
The story laid out here by Marc is much closer to what you would expect from Episode 3 rather than HL3.
> events following those described in my previous letter (referred to herewith as Epistle 2).
If 'Epistle 3' does not mean 'Episode 3', then 'Gertie Fremont' does not refer to 'Gordon Freeman'. That's what the author called it, whatever the internet at large thinks at any point in time is less relevant IMO.
You're right, must have missed that part. Regardless, whether it's HL3 or HL2:E3 I think it's safe to say it's not happening. I'd be surprised if Valve really is sitting on this project for the next big tech breakthrough they achieve. Hard to say.