Cad éan difríocht idir na frásaí: i ndiaidh sin
ina dhiaidh

FRC!

An rabhais in ann rith i ndiadh an timpiste? =Where you able to run after accident[after the] Suggests immediatly after event X, Y started or was relivent. Causal relationship?

(tar éis X) thosaidh sé ag rith sa seachtain ina dhiadh sin = he started to run in the week after that (after X occured) /started he running in the week after that [after that] Suggests some time after X happned Y started

Also: sheol na báidíní ina dhiaidh an long mhór =the boatíns sailed in the wake of the big ship. Suggest time and space difference, and non-causal relationship

I have also seen the likes of rith siad in bhur ndiaidh =they ran after us

Maybe you can have: i mo dhiaidh, i do dhiaidh etc

The Irish for "that" is really "é sin", not "sin", although it's commonly reduced to "sin". However, when it comes to posession, it always stays as "é sin".

at him: aige ( ag + é )
at that: aige sin (ag + é + sin)

Therefore you have:

Because of that = Dá bharr sin (i.e. De + a + barr + sin)
After that = Ina dhiaidh sin (i.e. i + a + diaidh + sin)

In the English language, we don't use posession directly with "that", i.e. the following sounds weird "I saw that's coat on the floor". (In my own dialect of English, we would say something like "I saw that thing's coat on the floor".) However, in Irish, you can use posession directly with "that", which can yield some strange looking sentences in the eyes of native speakers of English... here's an example from the inner cover of Irish passports:

Iarrann Aire Gnóthaí Eachtracha na hÉireann ar gach n-aon lena mbaineann ligean dá shealbhóir seo, saoránach d'Éirinn, gabháil ar aghaidh gan bhac gan chosc agus gach cúnamh agus caomhnú is gá a thabhairt don sealbhóir.

In English I suppose you could translate the underlined part as "the holder of this". Here's the official English translation which appears below it for those who are interested:

The Minister for Foreign Affairs of Ireland requests all whom it may concern to allow the bearer, a citizen of Ireland, to pass freely and without hindrance and to afford the bearer all necessary assistance and protection.

As you can see, the English version just says "the bearer" rather than "the bearer of this".

"I ndiaidh sin" isn't correct: to say "after that" you have to say "ina dhiaidh sin".

Ina dhiaidh = after it/him.

Táim caillte ceart anois

Cad chuige?

é sin - that (one), used on its own:
Cad é sin? What is that?

sin - this (after a noun, or a prepositional pronoun):
an fear sin - that man
aige sin - of that one,
chuige sin - to that one
faoi sin - about that (one)

a + X + sin (an X of that one):
a theach sin - the house of that person
ina theach sin - in the house of that person


Now 'diaidh' is a bit tricky - theoretically it should mean something like 'the space/time that's behind, the 'behindness' or 'afterness'' so:

i ndiaidh an fir - in the 'afterness' of the man, i.e. in the space behind the man; after the man
ina dhiaidh - in his 'afterness', ie. after him
i mo dhiaidh - in my 'afterness' - after me
ina dhiaidh sin - now, this is similar to 'ina theach sin' - in the 'afterness' of that (person, time etc.), ie. after that (one)

I hope this is clear
Daithí

Correction:

i ndiaidh an fhir

Sea, i ndiaidh an fhir. Botún cló atá ann, is dóigh :-)
Meastú an bhfuil an miniú seo liom sothuigthe?
Daithí

Tá sé sothuigthe... domh, ar aon nós! Níl ’s agam maidir leis na daoiní eile!