Stay, remain, wait, abide, tarry, linger can mean to continue to be in one place for a noticeable time.
Stay, the most general of these terms, stresses continuance in a place or sometimes in a specified condition; it often specifically connotes the status of visitor or guest.
Remain is often used interchangeably with stay but distinctively means to stay behind or to be left after others have gone.
Wait implies a staying in expectation or in readiness.
Abide implies prolonged staying or remaining after at length and usually connotes either stable residence or patient waiting for an outcome.
Tarry implies staying when it is time to depart or to proceed.
Linger, like tarry , usually implies outstaying one’s appointed or allotted time; frequently, however, it also implies either deliberate delay or disinclination to depart.