There are actually different definitions for different purposes so you need to look at each closely.
For bank lending rules, it doesn't matter if you've previously owned a house. The key is whether or not you (or either person in a joint application) has ever had a mortgage before, either in Ireland or abroad.
In tax legislation, the definition varies depending on purpose. Specifically for the help to buy scheme for example, you must not have previously bought or built a house. Getting an inheritance / gift of a house does not count.
"“first-time purchaser” means an individual who, at the time of a claim under subsection (3) has not, either individually or jointly with any other person, previously purchased or previously built, directly or indirectly, on his or her own behalf a dwelling;"