I have dry hands.
1. I think you should put on hand cream more often.
2. I think you should apply hand cream more often.
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Are both the same? Do you have some other verbs instead of 'put on' or 'apply'?
Both mean the same thing.
He put on his work clothes this morning.
(no "apply" verb form works like this)
She put on sunscreen before she went out on the beach.
She applied sunscreen before she went out on the beach.
They put on their thinking caps in math class.
They applied the recently learned concepts in today's math lesson.
(There lots and lots of variations!)