Strawberry smoothie and strawberry milk shake
Both can be rich. Smoothie can be lean. Milkshake has ice-cream, smoothie usually doesn't.
A smoothie is fruit/veggie based while a milkshake is ice cream based. Both are delicious!
So, basically, the strawberry milkshake is strawberry ice cream (or vanilla & strawberries) and milk. A strawberry smoothie is strawberries, some sort of liquid (usually juice), yogurt (sometimes people use a drop of ice cream), and ice. It's way more fruit and ice than a milkshake.
Also, protein powder, bee pollen and other such things are often now added to smoothies, but most probably not added to a milkshake which is usually a dessert (delicious with a burger).
We add a dollop of but butter to our smoothies and they taste a bit like milk shakes - amazingly delicious!