Ha, ha! This is a very fine point! As Anon has said, people will understand it either way, for both a) and b) BUT there actually IS a preference. You pull ALONG a curb, and you pull BESIDE another car. Honestly, I cannot claim to know why. However, I BELIEVE that it is due to the curb being immobile, and the car being mobile.
Certainly, this is a very minute distinction that doesn't always crop up in conversation. One could stand BESIDE one's immobile house, for example...yet one might direct a child to lay a garden hose ALONG the side of the house. So ALONG seems right when speaking of moving something TO PARALLEL something immobile. When the immobile object is used as a directional reference (like a curb is, when parallel-parking) then the word is ALONG. The act of pulling beside another car DOES involve making the sides of the two cars parallel, but the fact that the first car is mobile, could be located in ANY orientation, and in fact could still be moving, all seem to contribute to making BESIDE or NEXT TO more appropriate than ALONG. Very tricky.
For further confusion, you can consider the use of the nautical term ALONGSIDE, which is used when two vessels are brought side-to-side for transfer of crew or supplies, or for repairs, or to share berthing. ALONGSIDE could be used for the two cars, but not for the curb. It has a connotation of a more dynamic or hazardous operation, as in "Bert drew alongside Al's car so he could shout insults as they wove across the field together."