Follow, pursue, chase, trail, tag, tail are comparable when meaning to go immediately or shortly after someone or something.
Follow is the comprehensive term; it usually implies the lead or, sometimes, guidance of someone or something.
Pursue in its earliest sense implies a following as an enemy or hunter. The term therefore usually suggests an attempt to overtake, to reach, or to attain, and commonly in its extended senses, even when the implications of hostility or of a desire to capture are absent, it connotes eagerness, persistence, or inflexibility of purpose in following one’s thoughts, ends, or desires.
Chase implies fast pursuit in order to or as if to catch a fleeing object or to drive away or turn to flight an oncoming thing.
Trail implies a following in someone’s tracks.
Tag implies a persistent, annoying following or accompanying.
Tail specifically implies close following and surveillance <he employed detectives to tail the suspect>