Hi there! This is an extremely common question that gets asked regularly here. I don't actually have the time this afternoon to give you a fresh answer, but I've written in great detail about the subject matter before in this three part answer here, and also talk about it at length in this thread as well, and in this older answer also. Hopefully these answers will be illuminating for you.

The summary is that Irish immigrants were very much indentured servants when they were sent to North America, not slaves; there are substantial differences between the two systems and although conditions for indentured servants could be horrific and were highly exploitative, it is not necessarily the physical intensity of exploitation that characterises slavery as unique and distinctive, but rather the way in which slavery is constructed. At best, scholars argue that indentured servitude might be seen as a kind of 'proto-slavery'; a system that developed some of the institutions and principles that would later be used to make slavery a working and effective system of extreme exploitation, without ever becoming slavery itself. Indentured servitude and slavery existed alongside each other as distinct systems, with slavery eventually replacing servitude.

It is also important to emphasise that the idea that only the Irish were targeted for exploitation is a misrepresentation - in fact, Caribbean planters at least resented having Irish labour forced upon them and made active efforts to obstruct the arrival of Irish immigrants. Their preference was overwhelmingly for Scottish Protestant workers in the indenture period; the use of Irish labour reflects the political prejudices of the imperial government and difficulties in procuring the kind of labour preferred by the planters (whilst there were many Irish people sent against their will, the recruiters for indentured servants also saw Ireland as fertile recruiting ground for voluntary migrants, which in part explains the skew towards Irish labour in the indenture system).

Indenture is also a quite a minor phenomenon by the 19th century and is in decline in the 18th, having already been replaced by African slavery as the dominant system of forced labour; though it does continue, slavery begins to replace it meaningfully in the 17th century, and is a distinct system with its own legal and social construction by at least the mid point of that century. The exception to this rule is the British Caribbean where the practice undergoes a series of major revivals from the 1840s onwards - at that point however, the victims are Indian and Chinese workers from elsewhere in the British Empire, rather than workers from the British Isles. Irish migrants that arrive in the later period of the 19th century are not coming in as contracted indentured servants.

I am, as always, happy to take follow up questions if the linked answers leave anything unclear, though I am very busy today, and it might take me a little time to get back to you, so please be patient!