You're right about the first two functions being the same. And I can understand your confusion.
But look at the weaker functions in both systems. They are different. And that means you can't simply switch the types around.
Lets look at istj and istp.
In Socionics the functions go
Ti, Se, Fi, Ne for istj.
Si, Te, Ni, Fe for istp.
And in mbti the functions go
Si, Te, Fi, Ne for istj.
Ti, Se, Ni, Fe for istp.
Which means in mbti, the istj has Si as his strongest function and Ne as his weakest,
and then in Socionics the istj has Ti as his strongest and Ne as his weakest.
The mbti istp has Ti as his strongest function, and Fe as his weakest.
And in Socionics, he has Si as his strongest function, and Fe as his weakest.
So at least both systems agree on that much. istj is weakest in Ne, and istp is weakest in Fe.
But both types can't exist in nature, so one typology must be wrong. Or they are both wrong.
If an istj was to be moved around a lot in their job, having to adjust to new situations, just when they were starting to get comfortable and familiar in their job, and if they were being moved around a lot, they would not be happy campers. Their weak Ne couldn't handle it.
Too much change, too much uncertainty. An istp could cope though. Same with Fe. Someone breaks into song around an istp, and they will not get anything back. They may even tell you to stop singing. Weak Fe. Do the same with an istj, and they wont flinch the same way an istp would.
What I'm trying to get at, is that the weaker functions shouldn't be overlooked. It's not a simple switch.
Oh and mbti is wrong.

There is no such thing as a human who uses Ti as his leading function and Fe as his weakest.
That person is just a fantasy dreamed up by mbti.
The reason I know such a person could not exist, is that Ti needs Fe to balance it out.
If Ti was your strongest function, and Fe your weakest, inferiorest, most detestable, then Ti would take over and you would be a robot.
Oh and the personal example you gave about the grandmother and the child, to get your point across, suggests enfp to me.