Interesting, the two expressions are not totally equivalent when the variable itself is an Around
object:
In[1]:= Around[10, 1]*X + Around[20, 2]*X /. X -> Around[1, 2]
Out[1]= Around[30., 44.77722635447623]
In[2]:= (Around[10, 1] + Around[20, 2])*X /. X -> Around[1, 2]
Out[2]= Around[30., 60.0416522091123]