There would be no difference between a soldier and a West India Company soldier. This was the lowest military rank in the West India Company. Men were recruited and had no say as to where, that is, what colony, they were being assigned to. So those who came to New Netherland came by happenstance.
For more information on Soldiers please see: Jaap Jacobs, “Soldiers of the Company: The Military Personnel of the West India Company in New Netherland,” forthcoming.