It means the same thing. Achi is simply a combination of "My" (Sheli) and "Brother" (Ach). It's a shortcut, if you will.
sheli (שלי) means "my" or "mine"
The word "My" in Hebrew is pronounced: "Sheli"
lo sheli
to a female: yafah sheli (יפה שלי) to a male: yafeh sheli (יפה שלי)
שלי (sheli)sheli-shin,lamed,yod שליSheli, pronounced sheh-LEE, written - שֶׁלִי
ha'ah hanotzri sheli
Hayom yom huledet sheli
my apple = tapu'ach sheli (תפוח שלי)
Translation: tapuach sheli (תפוח שלי)
"My English" = ha'anglit sheli (האנגלית שלי)
"my children" = hayeladim sheli (הילדים שלי)
It means 'All that is mine'