Relation between field of two webform
As far as I know you can not reference a webform submission from another webform. The functionality you describe is needed here is something I recommend using standard Drupal content types for.

Create a content type called Vendor and another one called Sponsor. Use the module Entity reference to create a field that describes the reference between the content types.

Webforms are great for simple forms, surveys etc but not in this use case.