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Even at full speed, you can't tell the difference between NVMe and SATA in most use cases. The reason is that storage speeds are measured in MB/s, while your perception of how fast a drive is (how long you have to wait) is the inverse - sec/MB. Being the inverse means that the bigger MB/s becomes, the less difference it makes. And it's the smaller MB/s operations which make the biggest difference.

Imagine you're copying a folder with 100 MB of small files (documents), and 1 GB of large files.(movies). You have a NVMe SSD with 3 GB/s sequential speeds, 30 MB/s 4k speeds. And a SATA SSD with 500 MB/s sequential speeds, and 60 MB/s 4k speeds. Which is faster? Obviously the NVMe drive right? There's 10x more large file data than small, and it's 6x faster at large file speeds while the SATA drive is only 2x faster at small file speeds. So everything is in favor of the NVMe drive, right?

NVMe: (100MB / 30 MB/s) +.(1000 MB / 3000 MB/s) = 3.33 sec + 0.33 sec = 3.67 sec
SATA: (100 MB / 60 MB/s) + (1000 MB / 500 MB/s) = 1.67 sec + 2 sec = 3.67 sec

Surprise! They take the same amount of time. Because wait time is the inverse of MB/s, it's the smaller MB/s speeds (the 4k read/write speeds) which make the biggest difference in most use cases. And since 4k read/write speeds still aren't anywhere close to hitting the SATA 3 bandwidth limit, most of the time you won't be able to tell the difference between a SATA SSD and NVMe SSD.

The only time the NVMe SSD has a clear advantage is if you regularly work with lots of large files. Like video editing. Otherwise, you should just ignore the sequential speeds, and concentrate on getting a SSD with fast 4k speeds (NVMe or SATA). That will make a bigger difference in most uses cases than faster sequential speeds. All other things being equal, the NVMe drive will be faster than SATA. But SATA is usually cheaper and in most cases you won't be able to tell the difference. And if you're able to get a SATA SSD with faster 4k speeds because of the lower price, it may very well end up performing faster (albeit imperceptibly) than the NVMe SSD.

(Incidentally, the same problem occurs with fuel mileage. Fuel consumption is measured in volume / distance, so most of the world measures it in liters per 100 km. The US uses the inverse - MPG. This results in car buyers in the US obsessing over high MPG vehicles, when they actually make very little difference. Small improvements in the efficiency of low MPG vehicles (trucks and buses) OTOH make a huge difference in amount of fuel consumed. e.g. Going from 20 to 21 MPG (a 5% increase in MPG) actually saves you more fuel than going from 50 to 55 MPG (a 10% increase). And going from 6 MPG to 6.1 MPG (a 1.7% increase) saves even more fuel for the same distance traveled.)

Anyway to use with old mac air ssd?

I can't really follow your logic, but why exactly is your SATA slower at 4K than the NVMe?