You can just round the result, and then they are the same number.  

    Total[ E^(Round[list, 10.^-6]/t)]
    
    4 E^(-0.683013/t) + 3 E^(-0.183013/t) + 2 E^(0.183013/t) + E^(
     0.683013/t)

The `Exp` and `Round` function are listable, so you don't need an explicit call to `Sum`.  But if you wanted one, 

    Sum[ E^(Round[list[[k]], 10.^-6]/t), {k, Length[list]}]