No, there is only one master photo.
You have no control of the "external" photo however . The external recipient can add or change your photo,:
https://support.microsoft.com/en-us/office/add-change-or-remove-a-picture-for-a-contact-in-outlook-1717939b-6b15-48b5-a7b8-1effe238b3f3
However you can send them your contact info with a photo if you want. Whether they use that photo is up to them