Tail number is synonymous with registration number.
On civilian aircraft tail number refers to the registration number.
Not always. EASA gliders (and yes gliders are aircraft) with markings in compliance with EU regulation 1592/2002 carry the REGISTRATION on each side of the fusalage and under one (port) wing. The fin may be used for markings chosen by the operator. For gliders it may be the last three letters of the registration but is commonly a competition number that is a numeric or alpha numeric sequence allocated by the gliding movement and bears no relationship whatsoever to the registration.
See also UK CAA CAP 523.