If it's liquid soap yes, all soap is the same, just a different strength, for dishes than hand soap, which is milder, so use a little more. You can use laundry soap, also.
No, there is no health risk. All any soap does is make the dirt or in the case of dishes it is food residue, loosen up and move away easier. So either will help clean the dishes. You should always rinse your dishes well to remove any soap too.