No, typhoid fever is not the same thing as typhus.
Typhus is caused by microbes called rickettsiae and is carried by fleas, mites, and ticks, which in turn are carried by rats and other rodents.
Typhoid (also called typhoid fever or enteric fever) resembles typhus in its symptoms but is caused by a different microbe, Salmonella typhi, which is usually carried by food or water contaminated with human feces.
Both diseases cause fever, delirium, rashes, and coughs.