There is not much difference between the two except the price and the grade of oil they use.
Snowmobile 2 stroke oil is a higher grade of 2 stroke oil made for use in very cold temperatures so that it remains well mixed with the gas and doesnt separate in cold temps where as 2 stroke oil for weed wackers,chainsaws and boat motors is a lower grade oil made for use in normal temperatures where such separation doesnt occur.
As long as you follow the correct mixture ratio for your weedwacker you will be fine, I use Snowmobile 2 stroke oil in my 60HP Johnson outboard during duck and goose season because temps on the water in winter can reach 20 below zero and standard 2 stroke oil will begin to separate from the gas at those temps and settle in the bottom of the tanks.