No. Those with -one may be heard by native speakers as just slightly more formal than those with -body , but the difference is insignificant. The two groups are in free variation both in everyday conversation and in formal writing.
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hrsaneiEx. He is someone you like to go out with.They all sound fine to me whether with 'someone' or 'somebody'. The last one seems especially idiomatic to me with 'somebody'.
Ex. You shouldn't datewithsomeone you have met online.
Ex. Someone might think that you are crazy.