Companies market this as 1.5Gbps (lowercase b, as in bits. They use powers of ten instead of 8 to make it "easier to understand" and coincidentally more attractive).
Actually that's wrong too.
SATA uses 8B/10B encoding, hence it has some overhead, which sequentially limits the data transfer to 1.2Mbps = 150MB/s.
So 1.5Gbps = 150MB/s ONLY when referring to SATA. Consequently SATA 2 is 3.0Gbps = 300MB/s. Again these equations only hold true for SATA.
Sidenote: If you're getting a PCI card, you'll be limited by the PCI bus, which maxes out at 133MB/s.
You are partially correct, I forgot about the 8/10 encoding loss, though I think you meant 1.2Gbps=150MB/s
However, SATA does not actually work at 1.5Gbps, it works at 1.5 GHz, and the 1.5 Gbps is a result of companies simplifying things for marketing reasons.
OP, if you want it explained, the reason is that 8/10 encoding is 80% efficient, so SATA working at 1.5 GHz gives you 1.20Gbps bandwidth, which divided by 8 equals 150MB/s.
As I and nobly said, the PCI bus will limit you well below that. You would be extremely lucky to get 133MB/s out of the PCI bus (that is the theroretical shared bandwidth, so any other devices, including most older ethernet controllers and any other cards you have, are sharing that bandwidth).