Ask a child what the internet is and you will usually get a description of a phone. Ask an adult and you will often get a description of a browser. The three ideas here ... the network, the places on it, and the system that finds them ... get collapsed into one constantly, which is exactly why none of them can be explained properly until they are pulled apart.
So we pull them apart. The internet is the talking. A website is a place. A search engine is the thing that knows where the places are.
The internet is computers talking to other computers.
The internet is computers talking to other computers. Not a place, not a cloud, not a phone. Wires, radio signals, and a very large number of machines passing messages along.
A website is a place on the internet where somebody keeps their stuff so other people can come look at it.
A website is a place on the internet where somebody keeps their things so other people can come and look. Somebody made it on purpose, and that turns out to be the interesting part.
A search engine has already looked at almost everything, so it can tell you where to find what you want.
A search engine has already gone and looked at almost everything, so that when you ask, it can tell you where to go. What it shows you first is a choice somebody made.