At the time, + was used to require that something be present. Quotes were used to require words appear in a particular order. You could do a search where you quoted a phrase, but that didn't necessarily require it to be present (as I recall). If you absolutely wanted the quoted phrase to be there, you had to quote and put a + in front of the quoted phrase. So yes, they were different things.
When + was eliminated, quotes took its place. Quoting a single word was the same as when you used to + a word -- find the exact word. Quoting a phrase still meant find the phrase, but that also meant it was required to find the phrase.
With +, then with quotes and with verbatim, it's about what you retrieve. Verbatim says get these words or words and only those words. Quoting says get these words and only those words (and only those words in a particular order, if you indicate that). Just like + used to mean get these words and only these words.
The ranking of results might vary when you quote versus verbatim, but what you're asking to be retrieved is the same to us.
When + was eliminated, quotes took its place. Quoting a single word was the same as when you used to + a word -- find the exact word. Quoting a phrase still meant find the phrase, but that also meant it was required to find the phrase.
No, quoting did not take its place. At all. That's why verbatim was introduced, after outrage. Google claimed it did, but it still aliased. It still decided to provide results without quotes.
Again, this is why verbatim was born. From that "Google no longer gives precise results, ever" angst.
It wasn't. It isn't. I never has been. Ever.
Verbatim was introduced to replicate that lost + functionality, after massive outrage at the inability to find search results. The fact that you, and other Googlers still think "" is the same as verbatim/+, when it doesn't even show the same search results, is highly, highly questionable.
To be beyond blunt, you're wrong. You are completely and totally wrong. +/verbatim and "" are not the same thing.
Please go away, and learn how your own product works, before commenting on it, ok?