I think they have slightly different meanings where “use” is more direct like a tool and “utilize” is more indirect like a system but that could be more about context than meaning. The words “usage” and “utilization” show this more where I would expect “usage” to be binary or integer and “utilization” to be fractional or percentage. That context and expectation is important for clear writing.
I'm sure a lot of people would like this to be true, but it's right there in the definition of use: https://www.merriam-webster.com/dictionary/use. Anywhere you can use "utilize" you can also equally use "use." One subsumes the other.
Personally, anytime I see the word "utilize" it makes me think the writer is just trying to sound smart or "put on airs." For me it has the opposite effect that the writer is trying to achieve.
I agree that utilize is distinct from use, in that it makes something useful in a novel way; you might utilize a flat stone to dig, where you would otherwise use a shovel.
But I also agree with GP that many words like this are chosen just to sound more impressive, in the same way that people say 'at this time' instead of 'now.'