Donna,
Townlands, eg Ballybrannon (often Ballybrannan), are unique to Ireland. It has more than 60,000 and they are traditional Gaelic land divisions which pre-date the Norman invasion in the 12th century. A townland is the smallest administrative area of land in Ireland. They can vary in size from 1 acre up to 5000 acres, though most are between 50 and 500 acres. The whole country is divided into an invisible network of townlands. Many are rural, and there is not necessarily any town in a townland. Indeed some have no-one living in them at all, eg mountain tops and uninhabited islands. They were used as the basis of leases in the estate system, and subsequently to assess valuations and tithes in the eighteenth and nineteenth centuries.
Some townlands have been forgotten, some survive only on property deeds and other have given their names to towns and districts.
In rural areas there were no street names or house numbers (that is still the case in some parts) and your townland was sufficient to identify you or get a letter delivered. The postman, and anyone else who mattered, knew exactly where in the townland everyone lived. They survive today as important markers of local identity. (A townland is not the same as a US township).
A group of townlands makes a parish and a group of parishes makes a barony.
Ballybrannan is in the parish of Grange. Loughgall and The Grange are close together in Co Armagh. Castledawson is about 50 miles north in Co. Derry/Londonderry and Garvagh is another 20 miles north of that, in the same county. People did move around in Ireland especially if they were labourers or had a profession that involved movement eg stonemason, policeman, soldier but in the main they stayed put, especially farmers. They rarely moved unless forced to. It takes a lot of work to improve a farm, and you don’t readily give it up and move unless there’s a powerful reason. If you have strong evidence that your ancestors lived in all 4 locations then fair enough but if it’s just that the names appear to fit, then they may be different families. (There were 625 people named Bruce in the 1901 census of Ireland so not very common but there were obviously dozens of mostly unconnected families).
Ballybrannan is 152 acres of mainly agricultural land. In Griffiths Valuation (1864) there were about 15 farms and some labourers cottages. No-one named Bruce is listed. However there was a William Bruce farming there in 1832 according to the tithe applotment records. He had evidently gone by 1864:
http://www.irishgenealogyhub.com/armagh/tithe-applotments/grange-parish.php
In the 1901 census there were 16 houses in Ballybrannan and a population of 63.
http://www.census.nationalarchives.ie/pages/1901/Armagh/Hockley/Ballybr…
You ask why your ancestors might have left Ireland. I am sure they left for the same reasons that millions did. To find work, or better paid work. Ireland has very few natural resources (no oil, coal, iron ore etc) and so did not benefit from the industrial revolution in the 1800s, the way Scotland, England, the US, Canada & Australia did, which created hundreds of thousands of comparatively well-paid new jobs in new industries (coal mining, steel making, railways, ship building etc). So that was a big pull factor. There had also been a huge population explosion in Ireland going up from about 3 million people in 1750 to 8 million in 1830. There simply weren’t jobs for all those people. In much of Ireland the only employment was subsistence farming topped up in Ulster and one or two other areas with a bit of linen weaving. And then the straw that broke the camel’s back, along came the famine, numerous times throughout the 1800s. The worst period was when the potato crop failed almost completely 3 years in a row in the late 1840s, and then partially several more years after that.
Many labourers and small farmers were very much one crop dependant, because you could grow more potatoes to the acre than any other crop (a crucial factor in an island where there was a shortage of spare land), and they needed the minimum of maintenance, but as a consequence they had nothing else to fall back on when the blight attacked them, and because it was largely a barter economy they mostly had no spare cash to buy food. When the crop failed 3 years in a row, people ended up eating their seed potatoes, leaving them nothing to plant the next spring. It is estimated that during the years 1845 to 1850, around 800,000 people died of starvation or of a famine-related disease such as typhus, dysentery, scurvy or pellagra. A further two million people emigrated. Unlike earlier famines, in which the population recovers quickly from the catastrophe and continues to grow, the after- effects of the Great Irish Famine were such that the population of Ireland, standing at 8.2 million people in 1841, declined to 6.6 million in 1851. Fifty years later, Ireland's population was still showing a decline (down to 4.5 million), even though every other European country was showing a population increase. Ireland’s population did not return to its pre-famine heights until 1964. Approximately 8 million people left Ireland between 1801 and 1920 - the equivalent of the entire pre-Famine population. The population today is only around 6 million.
Other factors encouraged emigration, eg early mechanisation on farms. With new machines to turn the soil and plant seed, farmers no longer needed an army of agricultural labourers to help on the farm. So those jobs were rapidly disappearing. Likewise mechanisation had led to linen factories being set up in places like Belfast. These made home weaving uneconomic and so also upset the labourer’s family economy. Agriculture was the biggest single employer in Ireland, but it was mostly a barter economy. Few people had any ready cash save what they could make from weaving or any government sponsored work such as building new roads. So when the opportunity arose to get jobs with a regular wage packet, as opposed to a few pence from your father each week, the decision to migrate wasn’t really all that hard to make. So it was as much about economic betterment as anything.
In addition, the British Government often placed adverts in the press encouraging people to migrate to take advantage of land that was available overseas. (I have attached as an example an article from the Belfast Commercial Chronicle of 1st November 1828 offering lands in Upper Canada).
From the information you have given your family appear to have been Presbyterians, and their surname and general location goes with that (most Presbyterians were in the counties of Ulster). That background implies they are descendants of Scots who settled in Ireland in the 1600s. (Some 200,000 Scots moved to Ireland then, representing something like 15% of the entire Scottish population). It appears that having moved once, Presbyterian families took a philosophical move about moving again and were more willing to leave than what you might describe as “native Irish.” The vast majority of migrants from Ireland to North America in the 1700s were Presbyterians. Catholics didn’t start moving in large numbers till much later.
