Planed timber has a less absorbent surface, and is less easy for paint to adhere to. There are definitely paints that are designed to work better on rough sawn surfaces, rather than smooth planed surface. I think that the difference comes down to how the paint attaches itself to the timber and how it stays there:
Type 1 - stick for dear life to the surface, forming a barrier which is gradually eroded (tend to be more water-based, thicker), or
Type 2 - soak in as far as possible and stain/protect the timber (tend to be more solvent-based, thinner), or
Type 3 - some combination of the above
It's worth reading the label/datasheet carefully. Cheers, W2S