You need a 42mm or 44mm watch band. Neither the 40mm nor the 38mm will fit. Yes, it will work, but there is a space where the lugs don't reach the end of the slot where the bands fit. The bands remain locked in place, at least because of my tests.
If you're OK with that, you should be OK. Apple Watch Series 4, Series 5, and Series 6 come in 40mm and 44mm case sizes, so they're the same. As long as you get the same size for the new Apple Watch, the existing bands should fit seamlessly. This is because when Apple slightly increased the size of the Apple Watch case, they kept the same strap sizes.
Usually, any watch band will be compatible with any Apple Watch, however, there are some differences in which Apple Watch band you can use depending on whether you have opted for the large or small version of your Apple Watch generation. While Apple Watch has been around for many years, Apple has maintained the same ear design every year. Keep in mind that larger Apple Watches have longer strap options, and smaller watches offer shorter strap options. When you buy an Apple Watch band, you may need to specify which watch it is for, large or small, but you can usually get any of the bands for any of the watches.
Similarly, if you have a 42mm Apple Watch, all of your bands will fit the new 44mm Apple Watch Series 4.However, although Apple Watch Series 4, 5 and the new Apple Watch Series 6 come in slightly different case sizes of 40mm or 44mm, your old Series 3 and earlier bands will still fit. The new Apple Watch Series 4 has a larger screen thanks to thinner bezels and a larger body. These lengths can be added to the size of the Apple Watch to approximately equal the circumference of the wrist, plus or minus a few millimeters. While you can't beat the quality of the original Apple Watch bands, you can also shop on Etsy or Amazon for more exclusive designs at affordable prices.
The straps for the 38mm model can also work with the 44mm model, however, they probably don't fit well. Apple Watch sizes refer to the length from the top of the device to the bottom, not side to side. If you have an older Apple Watch Series 0, 1, 2 or 3, your straps should be for the 38mm or 42mm case. The 40mm Sport Loop watch band can fit wrists from 130 to 200mm, while the 44mm watch band can fit 140-220mm wrists.