The answer depends very much on the child's motor skills. Rollerball pens are preferable to fountain pens if children have not yet developed good and automated writing motor skills. However, if children are already achieving good results with the pencil, can dose pressure well and write fluently and rhythmically, then the fountain pen is a good choice immediately after the pencil.
Like school fountain pens, rollerball pens for children starting school should be tailored to their specific needs. This starts with non-slip grip recesses in special versions for left- and right-handers that are adapted to the child's hand and offer a secure grip. Because if pens are slippery, a feeling of loss of control quickly arises during use, which leads to a subconsciously firmer grip, which in turn leads to faster muscle fatigue. And it goes as far as an ink flow that is matched to the (low) writing frequency of children for quick drying of the ink on the paper.
None. The two terms are used synonymously.