A tagline is for the life of a brand, it usually sums up a thing such as a brand.
A slogan is more of an advertising campaign spearhead, more product/service specific.
A Motto “saying” is more of a political, religious or philosophical guideline, expressing an important ideal.
E.g. “Don’t be evil.” (a philanthropic corporate motto of Google which was dropped in 2009)
Straplines, Throwaway lines
A Strapline, derivative of an advertising slogan, others include throwaway line, secondary heading. These terms somewhat weakly undermine the solid sense and true nature of the words slogans and taglines.