That depends who's doing the talking. You're a large business with a dedicated connection and your own network engineering team? Yeah, totally matters.
You're a single consumer, or a small business? Your dialog is limited to "Yes, I switched the router on and off. Yes, my local network works. No, I can reach the website over my phone, this is your problem".
Repeat three times, then get the inevitable reply of "it'll be up again in the next 24 hours".
Unless you're a network engineer, this really doesn't matter.
You're a single consumer, or a small business? Your dialog is limited to "Yes, I switched the router on and off. Yes, my local network works. No, I can reach the website over my phone, this is your problem".
Repeat three times, then get the inevitable reply of "it'll be up again in the next 24 hours".
Unless you're a network engineer, this really doesn't matter.