Hi, Rebecca -
Yes, cotton satin and cotton sateen are the same fabric. Technically, when it's cotton, the fabric is called "sateen" (satin is made from silk, rayon, etc.) Actually, "satin" just refers to the weave. The weave of "sateen" and satin are the same.
In place of cotton sateen, you can use a good high count cotton muslin. If you have a specialty (locally owned) quilt shop nearby, ask to see their cotton muslins, and ask them to show you their highest thread count cotton muslins. You can, for example, use a good kona cotton. I personally prefer those to cotton sateen for needlepainting, if I'm going to use cotton. If you can find a high count, good linen, that would be even better! Linen is much more resilient, esp. if you have to take out stitches.