I was wondering since the swashbuckler is able to store their Panache points as grit points, does that mean they automatically gain access to gunslinger deeds(since grit is a gunslinger ability)?
No.
In an honest effort to be more helpful... you can take the Amatuer Gunslinger feat for 1 Grit/day, and a 1st level Gunslinger Deed for which you otherwise qualify.
And, since Grit and Panache are the same Pool, you would get 1 extra point from your Wisdom modifier, in addition to all the Panache associated with your Charisma modifier, each day.
Both your Swashbuckler Deeds and your Gunslinger Deed could then be ran off the same Pool, yes.
Even though Amatuer Gunslinger only gives you 1 Grit point... you could use every point in your Panache pool fueling the Gunslinger Deed you get with the feat.
To my understanding, at least.
Multiclassing into gunslinger would allow the swashbuckler to use their panache points for gunslinger deeds which require grit, and to recover panache by killing someone with a gunshot like grit recovers. Or perhaps a feat for one deed as VM suggests. They don't have access to gunslinger deeds absent one of those though.
Thank you for the help. That makes more sense now.