The difference between benutzen and nutzen in German is subtle, but they have different nuances:

benutzen → To use a tangible object

1. Implies physical use of an item or tool
2. Often refers to manipulating or operating something

Examples:

1. Ich benutze mein Telefon. → I use my phone.
2. Benutzt du den Stift? → Are you using the pen?
3. Er benutzt den Computer. → He is using the computer.

nutzen → To use something abstract, to take advantage of

1. More abstract, refers to making use of opportunities, advantages, or resources
2. Often implies benefiting from something

Examples:

1. Ich nutze das Internet. → I use the internet.
2. Wir nutzen die Zeit. → We use the time.