【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>