Touring car and tourer are both terms for open cars (i.e. cars without a fixed roof). "Touring car" is a style of open car built in the United States which seats four or more people. The style was popular from the early 1900s to the 1930s. The cars used for touring car racing in various series since the 1960s, are unrelated to these early touring cars, despite sharing the same name.
"Tourer" is used in British English for any open car. The term "all-weather tourer" was used to describe convertibles (vehicles that could be fully enclosed). A popular version of the tourer was the torpedo, with the hood/bonnet line level at the car's waistline giving the car a straight line from front to back.