Most of the Irish stuff was destroyed in the 1922 fire. Post 1858, some wills were filed in local probate offices first, rather than the central office in Dublin, so the local copies survive but I would have guessed that they follow basically the same process as England & Wales. Other possibilities are that
extracts and/or summaries of wills survive in Dublin's Registry of Deeds documents. I would, however, class those as Registered Deeds (the images are on FamilySearch) that happen to be of a certain sub-type.
Re England & Wales: I've always equated Wills with Testaments. (The classic wording is "This is my Last Will & Testament..." though I have an idea that legal historians can explain how, centuries ago, wills and testaments were different...)
Letters of Administration are liable to confuse if you make the mistake of reading the documents concerned! Genealogists tend to refer to Letters of Administration (aka Admons) only when there is no will. However, there is
always a grant (aka letters) of administration to the executor - otherwise, they have no authority to act. I have never sat down and looked at the difference in wording between a grant where there
is a will, and a grant where there
isn't a will. So the classic cases are
- A Will (usually with a grant of administration attached);
- An Admon (i.e. a grant of administration but no will);
- An Admon with Will attached which is basically an ordinary will but where all the executors are dead or decline to serve. Or you could reverse it and say that it's like an Admon but with a will...
There are other documents - Inventories appear in earlier years, whether there is or isn't a will. Also, England & Wales can have Bonds where the executors promise faithfully to carry out their task on pain of a penalty payment to the local bishop (pre-1858).
There are also various Calendars and "Act Books" (similar to Calendars) listing "transactions" relevant to wills and probates. In
most cases, if there is no will, there is no benefit - certainly not in post-1858 England & Wales - of getting a copy of the Admon since it contains no more than what's in the Probate Calendar.
I
think that the grant of administration equates to the Scottish Confirmation.
Does England have a Testament Testamentar and/or a Testament Dative? Well, in my experience, no because it doesn't bother to give a name to what is actually just a bundle.
If anyone can refine any of the above, comments will be gratefully accepted.