Historically the Anglo-Irish, or at least the upper echelons, were a landed class. Thus you found them as landowners throughout the country. The richer and more fertile parts of the country had a greater conscentration of landowners and, therefore, of Anglo-Irish. You also found them in Dublin, where they dominated the professional classes, and the upper ranks of the commercial and bureaucratic classes. The suburbs and vicinity of south Dublin was where they tended to live. South Dublin is now much more intensively developed, and the presence and impact of the Anglo-Irish is much reduced.
By the early twentieth century they no longer had commercial dominance. Nor did they dominate most professions. (They were probably over-represented at the upper reaches of business and the professions, but not dominant). They continued to dominate the administrative establishment. Land purchase (by tenants) meant that, while the continued to occupy big houses and demesnes throughout the country, their economic and social importance was much reduced. Their decline was accelerated after independence, when they lost their domination of the administrative classes, and declined still further as landowners. Many, moreover, felt forced to choose between the “Anglo” and “Irish” aspects of their identity, and chose Anglo. The officer class of the British army was a traditional haven for many Anglo-Irish younger sons; many of them stuck with the British army and left Ireland. Or their children left Ireland. Ireland had continued high emigration for decades after independence, and the Anglo-Irish were probably over-represented among emigrants (though they wouldn’t necessarily have thought of going to Britain as “emigrating”).
Anglo-Irish is not really a synonym for Protestant. For a start, Presbyterians and other dissenters were not normally considered Anglo-Irish; they were stereotypically Anglican. More to the point, though, “Anglo-Irish” implied middle or upper class. Working-class protestants, who were numerous, were not normally considered Anglo-Irish.
“West Brits” are not the same thing either. West Brits could be Catholic, and indeed stereotypically were. “West Brit” (or “West Briton”) was a term of abuse for an Irishman who identified with and supported the British establishment in Ireland (usually, it was implied or stated, because it was materially advantageous to do so). West Brits were not assumed to be prosperous, but rather were thought to hope for prosperity.
And, of course, we mustn’t forget Brendan Behan, who famously defined an Anglo-Irishman as “a Protestant on a horse”.