What is this 'one colour' design trend and how can I reproduce it using a stock photo?

I had thought that the current trend towards 'one colour photos' was being called 'monochrome' but can't seem to find any examples.

The attached picture illustrates what I am referring to. The photo has been darkened and edited to match the colour palette of the website.

What is the best way to achieve this in Photoshop from a source jpeg. Bonus points if it can be done without leaving illustrator.

Is this likely to be a colour overlay layer style with a blend mode?