How different is Irish Gaelic from Scottish?
They're different enough to be considered separate languages (though that's more often a sociopolitical distinction than a linguistics one!), especially in spelling. However, when speaking slow, it's likely that both parties could make themselves understood without switching languages. Especially if the Irish speaker has a nice Donegal dialect.
They share many words, but from my understanding, someone talking Irish and someone talking Scottish Gaelic wouldn't really be able to hold a conversation. Wikipedia have a page on the comparison of Irish and Scottish Gaelic
Possibly true but many of my irish speaking friends claim to be able to understand it spoken.
It has also been said that "Scots gaelic becomes a lot easier to understand after a couple of drinks"- not being racist here repeating this- it is actually a very apt description of the phonetic difference Irish gaeilge and scots gaelic. The slightly slurred sound of gaelic is actually quite beautiful
The Gaelic languages (Scottish, Irish, and Manx) are all quite similar, but not one hundred percent mutually intelligible. That said, if a Scottish speaker met up with an Irish and Manx speaker, they could all talk together, although it may be a bit hard to understand them.
My mum is a Donegal (Ulster) Irish speaker; she says that she can piece together the meaning in writing for the most part (not to say that the spelling isn't often quite different, but nevertheless), and can understand some simple spoken sentences, but hearing Gaelic speakers speaking casually, she can't really follow along outwith the more fundamental vocabulary (which she says tends to be more similar to the Irish). She can't follow along with the Gaelic radio programs or anything like that.
That said, this is on the basis that she's never actually tried to learn, but just been exposed to it. Obviously an Irish speaker is going to have a very easy time of learning Gaelic compared to an English speaker ;) They're certainly similar languages, if just not quite mutually intelligible for the most part.