In all states, presidential elections usually meant a separate run of tickets featuring only that office. Presidential portraits on such tickets became another useful way of associating the required other tickets with the presidential ticket. We can imagine how those images created a sense of shared identity between the voters who carried the ticket portraits and the candidates pictured. The portraits also ensured that both observers and voters understood who was voting for whom. Sometimes vice presidential candidates were pictured, but not often. 
This 1868 Republican ticket from San Francisco’s eighth ward presents in curved display the names of the Party’s chosen members of the Electoral College and the city and county candidates. Curved or spiral presentations were largely successful in preventing “pasters” from substituting non-party candidates on official party tickets by pasting on the ticket alternate names. 
This ticket combines elaborate imagery with vivid colors (originally perhaps a bright red and an equally bright green). Seeing the color of the ticket or the images on the ticket of each Grant voter would certainly have been an easy political assignment.