No, the phrase in the letter would make the recusal more expansive.
Confirmation hearing:
I believe the proper thing for me to do, would be to recuse myself from any questions involving those kind of investigations that involve Secretary Clinton and that were raised during the campaign or to be otherwise connected to it.
Written statement:
I have decided to recuse myself from any existing or future investigations of any matters related in any way to the campaigns for President of the United States.
The phrase from the letter, "matters related in any way" is far more extensive.
Sessions is recused, from his own words and deeds, in matters related "any way" to the campaigns.