Is there a different amount of radiation that comes from regular cell phones compared to smart phones?

Depends on phone. Cell/smart phones all have ratings with the sar ratings based on the electomagnetic radiation they emit in use. All must be rated <1.6w/kg and the ratings are readily available. I see some rated from.24-1.55 from the same company. Check with your retailer or phone site.
Not a valid question. This is not a medical question.