“Soft” is the opposite of hard. It can be used to describe anything.
E.g
“This sweater is soft.”
“This bread is soft.”
“This cat is soft.”
“Smooth” usually means the top layer of something and talks about the feeling of something.
E.g
“Her skin is so smooth.”
“The frosting on the cake is smooth.”
“The ice is smooth.”
Let's try a few examples to see if we can see the difference.
I sleep on a smooth pillow.
- not scratchy, it feels good
I sleep on a soft pillow.
- not hard, my head falls into my pillow
The pilot made a smooth landing.
- not bumpy, you could hardly feel the touchdown
The pilot made a soft landing.
- the same as above, but not used as often
He is a smooth talker.
- an idiom; he talks persuasively, he is very convincing and gets what he wants
He is a soft talker.
- not used. Though you could say: He talks softly. Which means quietly.
The baby's hands are smooth.
- no wrinkles, your hands glide over the baby's hands as you touch them
The baby's hands are soft.
- about the same; but moreso pleasant to the touch
He runs with a smooth stride.
- not jerky, gliding, efficient.
He runs with a soft stride.
- not used
That's a smooth bourbon.
- I know that's a phrase, but since I don't drink bourbon I really don't know what that means.