A person with thin skin is someone who’s sensitive in nature. He/she is easily offended or hurt by criticism, disapproval, or any manner opposite to what he/she considers as gentle and kind.
Being soft is different from having thin skin, although they are commonly misused, depending on how it’s used as a description. When you describe someone as soft, it can mean lots of things — sensitive, caring, weak, insecure, pleaser. And mostly, these words can also describe someone who has thin skin. As opposed to a person with thick skin, they wouldn’t feel a knife to their back because they’re used to the pain or they didn’t expect people to treat them nicely.