First, If you look carefully, I think your new tires will say 1609 # max AND 44 psi max (Not "at".)
There are several tire standardization bodies throughout the world. In the US it's the Tire and Rim Association (TRA). In Europe, it's the European Tire and Rim Technical Organization (ETRTO). These folks set the load vs inflation pressure curves.
The load curves are size specific - that is for a given size there is a curve and it is unique to that size. However, there has been some standardization (that's what they are supposed to do) where tires with similar load capacities now have the same load capacity.
TRA and ETRTO sizing standards are slightly different (aside from the metric vs english dimensions). TRA puts a letter in front of their sizes where ETRTO does not. Plus (due to the metric thing) TRA P metric tires have a maximum pressure of 35 psi for standard load and ETRTO has a maximum of 2.5 bar (36 psi) for standard load passenger car tires.
HOWEVER (and this is where your question gets answered), there are ceratin circumstances where using more inflation pressure is called for - high speed operation for one. ETRTO called for optional maximum pressures of 3.0 or 3.5 bar (44 spi and 51 psi). As first steps in having a world wide tire standard, TRA has adopted these optional maximum pressures. (Technically, this is exactly right - more inflation pressure for high speed operation is the same regardless of where you are in the world.)
HOWEVER, the load curve is unchanged. It ends at 35 psi (or 36 psi) if you have a standard load tire.
Hope this helps.