I'll try to add a little to @StepanS's answer. As @StepanS said, there are two types of fields in a form, SharePoint fields and Common fields:
SharePoint fields that are automatically loaded from the list. When the form is saved, the data from these fields is saved in a list item. The only way to create a field like that is to add a column to the list in SharePoint.
Common fields that are created in the Designer and have no corresponding SharePoint columns. The data from these fields isn't saved in SharePoint, so they are usually added for the user's convenience and managed with JavaScript.
Common fields are actually easier to migrate between the lists, you just need to copy their code to a different form. To migrate a SharePoint field you have to first add a corresponding column to the target list.