What is the difference between the two adjectives "nützlich" and "sinnvoll", when both of them mean "useful"? Could you please give some examples?
As often in German, you can to split those two words into their pieces and analyze what they are about:
nützlich — es ist von Nutzen → it's of benefit/advantage
sinnvoll — es ist voller Sinn → it's full of reason
Most times, things that are full of reason tend to be beneficial so you can use those two words interchangably. There is a difference about plan and outcome, however:
Mein Plan ist sinnvoll. – Gut.
Mein Plan ist nützlich. – Wofür?
Dieser sinnvolle Plan war sehr nützlich. – Gut.
Dieser nützliche Plan war sehr sinnvoll. – Hä?
A fixed phrase you may encounter:
Mach dich mal nützlich! (Come on, help us!)