What the heck? I'm confused because I thought H4 and 9003 were the same bulb? Is there a difference?

Yes, you're confused. So are they-- the H4 is interchangeable with the 9003/HB2. That "X is for motorcycles, Y is for cars" seems to have come out of thin air.

The nominal spec on HB2 is 1500/910 lumens at 12.8v in the US reg, and 1650/1000 at 13.2v and 1250/750 at 12.0v. If we use the standard 3.4 exponent for light change with voltage change:

Start with 1250/750 at 12.0:

At 12.8 the math gives us 1557/934 (that is 3.1%/2.6% off from nominal spec at 12.8v)

At 13.2 the math gives us 1728/1037 (that is 4.7%/3.7% off from nominal spec at 13.2v)

Start with 1650/1000 at 13.2:

At 12.8 the math gives us 1486/901 (that is 0.9%/1% off from nominal spec at 12.8v)

At 12.0 the math gives us 1193/723 (that is 4.5%/3.6% off from nominal spec at 12v)

Start with 1500/910 at 12.8:

At 12.0 the math gives us 1204/731 (that is 3.7%/2.5% off from the nominal spec at 12v)

At 13.2 the math gives us 1665/1010 (that is 0.9%/1% off from the nominal spec at 13.2v)

However, the US reg has a ±10% allowable tolerance, the UNECE reg has a ±15% allowable tolerance (that is, the H4 has a wider range of allowable output). The US-spec also has a tighter filament precision tolerance-- and it's filament precision that gets you better focus.

However, nowadays when you get the high-performance bulbs from Philips you're getting that precision in either designation. And, despite CandlePowerInc (no relation) saying differently on a product page, they themselves say that "In areas where there is no legal preference for 9003 bulbs over H4 bulbs in cars,

any H4 or 9003 bulb can be used with confidence in any headlamp. (That .PDF on the similarities/differences is good enough for an overview without being too esoteric or arcane.)

Just like pretty much any other store, their goal is to make money. They're not immune from selling lighting-equipment shaped toys, so be careful what you "Add to Cart".