Each effect will apply to the OTHER character:
>Char1 and Char2 enter a matespritship.
>Char1's Matesprit eff: +10 Grit
>Char2's Matesprit eff: Attach a basic equipment from the deck
Char1 gets a basic equipment attached to it from the deck
Char2 gets +10 grit
Another thing I should probably specify; Some Matesprit effects only happen at the time in which that character enters the matespritship. Some examples are Tavros and Sollux. Their effects don't continuously go on for turns and turns; only the initial time where they entered a matespritship. Another thing I should specify: Terezi's ability: "Cleaning The Thinkpan" WILL trigger Sollux/Tavros's effects. This is because technically, they are entering a new matespritship.