The GE/PW Alliance is just really the brand name for the engine featured on that site.
However, I would not rule out a more formal merger between the companies eventually.
The competition to provide powerplants for the B777 has been bruising. R/R got off to a bad start, not helped by BA's strange choice for GE90's for their initial order. At the same time, BA sold their engine overhaul plant in Wales to GE.
Many were writing off R/R in the big civil engine market, but they clawed themselves back to get a very respectable 38% of B777 orders.
You can be sure that it's been not much less bruising for GE and PW.
So now another big programme comes along, the A380, probably the last 4 engined airliner. So it makes perfect sense for PW and GE to do a joint project to maximise profits and avoid tearing lumps out of each other.