Sphere will "manage" the organizational record differently for a form (through Communities > Forms: Single Step Donation ) and an event (through Communities > Special Events > Friends Asking Friends > Kintera Thon).

Only a donation form supports Organizational contact records.  This is evident through the Bookkeeping section, when selecting the existing "Org" through search or by selecting the 'Organizational Donor' radio button for new gift entry.

Registration forms do not support Organizational Records.

FAF or Thon events do not support Organizational records for donations (or the gift entry link) or registrations.  It does support organization records through Sponsor entry.