Jesus touches the dead body, which in the eyes of the Law made Him unclean. Burying the dead was a good deed, and so there were things that justified becoming unclean. And of course His touch is more powerful than death and its defiling power. But it would be rather startling to Jairus to have a stranger touch his dead.
The woman with the hemorrhage is ritually unclean. How does she dare touch Jesus' clothes--she would make them unclean, and by contagion him also? She knows He can do miracles, but that means He's holy.
When Jesus asks who touched Him, she has to admit this before everybody. Of course, instead of chewing her out He told her that her faith had made her whole and that she should go in peace. But why did He ask her to fess up? Maybe to heal her guilty conscience too? Or was He making a point about the cleansing He provided?