Good question. It is used in English because that is what the Spanish called themselves, conquistador(es). Your usage engram shows the earliest English use in 1830, but that is probably wrong. I'm pretty sure that in the late 16th and early seventeenth century the English had already borrowed the term. For example, I think Hakluyt's Principal Navigations uses it in places.

As to the second part of the question, other colonizers didn't necessarily view their efforts as conquests. In part this is due to cultural differences between Europeans and in part it has to do with indigenous groups in the Americas. For example, French and English colonists either didn't consider indigenous land tenure to be valid or they 'bought' lands to settle.

That said Jorge Cañizares Esguerra has argued that English colonization shared more with Spanish conquest than contemporaries or historians have acknowledged, see his Puritan Conquistadors.