Differences between 'Add existing field' and 'Add new field'
Add new field is used to create a new field; Add existing field is used to connect the existing field with another content type.

I don't think it's a big difference but it's a good option for developer to attach their fields to other content types. For existing field, after you have created the new field, you can attach that field to multiple content types. 

See also When should I use an existing field?