Neuroimaging studies have reported overlapping neural circuits for cognitive control when engaging in tasks that involve verbal and nonverbal stimuli in young adult bilinguals. However, no study to date has examined the neural basis of verbal and nonverbal task switching in both monolinguals and bilinguals due to the inherent challenge of testing verbal task switching with monolinguals. Therefore, it is not clear whether the finding for overlapping networks is unique to bilingualism or indicative of general cognitive control. To address this question, the current study compared functional neural activation for young adults who were bilingual speakers of English and French or monolingual English speakers who had limited French learning experience (“functional monolinguals”) on verbal and nonverbal task switching. Analyses showed common variance explaining general cognitive control in task switching across verbal and nonverbal domains for both groups, in line with the explanation that task switching involves general cognitive control, as well as unique brain regions recruited by monolinguals and bilinguals. Specifically, beyond the processing common to the tasks, monolinguals also recruited distinct networks for each of verbal and nonverbal switching but bilinguals used a common shared network. Thus, the domain-general aspect of switching is different for monolinguals and bilinguals.