These sisters have become the Sisters of Mercy of Alma?

[DameAgnes]

is that correct? Amazing story of their beginnings. https://aleteia.org/2017/07/17/sisters-of-mercy-their-cloister-was-the-alley-of-the-poor/

[krissylou]

That's about the foundings of the RSM.  This includes the Sisters of Mercy of Alma but it's bigger than just that community.

A ton of active women's orders organized themselves in diocesean communities (e.g. the Nashville Dominicans) and of course they were all friendly with other communities in their order but they were organizationally separate.  At one point there were (at least) three different Sisters of St Joseph communities in Massachusetts alone!  And they were all on good terms with each other but the Boston community was organizationally separate from the Springfield community, etc.

In more recent years a lot of those diocesean communities have merged.  So there's still a Sisters of St. Joseph of Boston and a Sisters of St Joseph of Springfield but several communities throughout the central United States (Cleveland to Louisiana!) merged about a decade ago to form The Congregation of St. Joseph.  I'm guessing that in time a bunch of other diocesean communities may join in this one too.  (Or maybe not.  Just a guess.)

The RSM were been structured the same way.  I knew a sister who was part of the Detroit RSM congregation.  After Vatican II a new diocesean community was formed, the RSM of Alma, largely out of a concern that many of the other RSM congregations were veering off in too liberal directions and the RSM of Alma wanted to be more traditional.  But at that point there were many organizationally separate RSM congregations, with their own leadership, etc. and one of them was the RSM of Alma.

Is there a Mercy Hospital near you?  It was likely established by RSMs.

More recently all the other American communities have merged to form the Sisters of Mercy of the Americas.  The Alma community chose to remain independent.

So all of that is to say, yes.  The RSM of Alma trace their history back to Mother Catherine MacAuley.  But it isn't just them, there are many other RSMs beside the Alma community.

[Nunsuch]

A number of the Mercy communities merged into the Sisters of Mercy of the Union in 1929. In 1991, they and all except 2 autonomous Mercy communities in the US (Alma and a small group of 12 older sisters in Maine) became the Sisters of Mercy of the Americas. A history of their 25-year history was recently published. 

On the history of the Mercys' arrival in the New World in, you may be interested in a documentary that can be seen in its entirety on YouTube. This covers the original foundations from Ireland. I'm not being allowed, for some reason, to post the link, but you can search on YouTube for "Going West on the Journey" and you will find the film (about 40 minutes). It can also be found here: 

http://www.screencast.com/t/Os7PPAm7