When it comes to correlation, the cognitive type will correlate with either the MBTI type or the Socionic type but not both. You have to choose between MBTI or Socionics which system you want to go by in order to correlate with your cognitive type. Any comments are most welcome.
I am not sure about what you are meaning. Ignoring the definitions of the various systems, you have a FiSe in mbti (ISFP) and a FiSe in socionics (ISFj of ESI or even other names). You can safety estabilish an one to one relation.