AFAIK a 'twitcher' is very much concerned primarily with spotting rare birds and generally ticks off lists of sightings ... often seen in newspapers and on tv crowded into an area (even peoples back gardens!) to view a bird blown off course etc.
A 'birder' would be more just interested in birds specifically but not necessarily travel miles to see a rare(er) species.
Of course someone else will come along and trash all of that!
Sounds about right, I've peered into a few gardens in my time
. I've not done that many twitches of late, I just can't be bothered with the 'new' birders who seem (to think they) know it all, that and the cost of twitching these days. In the 80's whilst on St.Mary's, Scilly Islands we were watching a myrtle warbler (an American species) when the CB radio in someone's hand crackled "Wilson's Warbler, Rame ,Cornwall" (a first for UK and indeed the Western Palearctic) within seconds the crowd had dispersed and were trying to get back to the mainland, one of the crowd Ron Johns IIRC, decided to charter a helicopter to get him off the island and onto Rame to see the bird, I don't know if he did get it or not. I've done: Cardiff to Cley ,Norfolk to Ramsgate (?) to Newcastle and back to Cardiff over a weekend, Cardiff to John O'Groats in 48hrs (and dipped!!(missed the bird)) and a few jaunts to Ireland before now. Twitchers would generally have initially been birders who have allowed their hobby to evolve into twitching. The name, from what I've been told comes from nervous twitches when waiting for a bird to show., but I would stand corrected. There was and probably still are rivalries if you like, between birders and twitchers and birders, twitchers and photographers.
Then there's the 'stringer', he can be a birder,a twitcher or possibly even a photographer, he just can't tell the truth and makes up his sightings but never has any evidence nor anyone else sees his birds. Followed on by the suppressor, he genuinley finds stuff but only tells his inner sanctum or tells everyone after the bird has moved on, not a nice guy.
Watched a TV documentary years ago about a twitcher called, I think, Lee Evans. I've got no interest in birds at all but it was a fascinating insight into obsessive behavior!
GC
Met Lee (AKA 'socket') a few times over the years, he's a bit of a marmite type of guy, but I like him, he's a bloody good birder and knows his stuff. Found me a few ticks on my first visit to North Norfolk back in the day.