Based on my understanding of the way the record is structured, Arch Dixon was the employer of Peter Dixon. Most likely his former slave master, but since this is post Emancipation, he is now a freed man. Odds are that Arch Dixon was the one who gave his name to Peter Dixon, but is most likely not a relative.
In looking at this in more detail, the "Freedman Bank" was a Savings and Loan put in place by Lincoln to give freed slaves a place to invest their money (since many institutions wouldn't take their money).
http://search.ancestry.com/search/DB.aspx?dbid=8755
