The answer is no, according to a Q&A on The New York Times website discussing whether bar soaps are more likely to spread germs in a public bathroom.
According to the article, the most rigorous study of this question was published in 1965.
Scientists conducted a series of experiments in which they intentionally contaminated their hands with about five billion bacteria.
The scientists then washed their hands with a bar of soap and had a second person wash with the same bar of soap. They found that bacteria were not transferred to the second user and concluded: “The level of bacteria that may occur on bar soap, even under extreme usage conditions (heavy usage, poorly designed non-drainable soap dishes, etc.) does not constitute a health hazard.”
A 1988 confirmed these findings. researchers inoculated bars of soap with E. coli and Pseudomonas bacteria and had 16 people wash their hands with the contaminated bars. After washing, none of the subjects had detectable levels of bacteria on their hands. The study concluded that “little hazard exists in routine hand washing with previously used soap bars.”
According to an article on the “How Stuff Works” website, there is no real difference between the two. All types of soap are composed of the same essential components — alkali salts of fatty acids and detergent properties.
Rethinking Carpeting's Role in Senior Care Facilities
Parkview Health Breaks Ground on New Hospital in West Lafayette, IN
Loma Linda University Health Experiences Data Breach via AI Tool
Inside One of Healthcare's Most Ambitious Hospital Projects 
Turning Condensate Loss into a Systemwide Steam Efficiency Opportunity