The Palm Town manga continues in the same vein as the Maple Town manga. Short, zany adventures that differ greatly from the tone set in the anime. It's never explained why Patty moves to Palm Town, nor do we see her leave Maple Town. I guess you are expected to get this information from watching the anime.
You know how the anime really avoids using puns or doing anything too Japanese, to make it easy translating it for other markets? The manga is pretty much the opposite, and the Palm Town manga especially have a great love for puns, making it quite a challenge to translate. I tried my best.
And now, the Palm Town manga (reads right to left):