"Impeachment", both etymologically and legally, is a nondescript descriptor, conveying whatever meaning and legal importance any particular society allows it to have at any one time. In legal terms it is therefore simply the equivalent of placing an impediment in the way of a public official before they do more potential damage in what up to that point has been a legally unchallenged manner. In older English law, as the examples above illustrate, it was a method whereby people "above the law" could be brought back within it and charged, and it is in this sense that it was resurrected also in the USA. But like in England, it is worth noting that impeachment is conferred by a vote within the political house of representatives and has nothing to do with any other legal arraignment or indictment which may be levelled against the person arising from the same perceived "crime" they may have committed. In other words it has all the legal effect of a censure, which is basically none at all unless followed up with actual legal charges. There is no "archaic English law" therefore that could be used to topple Trump, more's the pity but there you go.
Even previous US impeachments of presidents don't have much bearing on Trump. Bill Clinton, for example, was impeached twice over on the same day - once for perjury and once for obstruction of justice. However no charges were legally levelled against him related to these indictments, so it meant diddlysquat, and Clinton rightly or wrongly chose to interpret his stance as president as one in which to respond with resignation despite lack of indictment would set a very dangerous precedent in which accusation itself was enough to dethrone the sitting chief executive of the state. So he simply carried on. The same for Andrew Johnson who was impeached for vetoing an Act designed to limit his powers and which itself was deemed unconstitutional afterwards (meaning more or less that he had been in the right all along, despite the impeachment). He also simply carried on, and probably would have whether the subsequent narrow "acquittal" also voted by the house hadn't also served to support his decision (Clinton didn't even get that much peer support for his stance).
Trump, if he continues as he's started, will almost certainly be impeached. Probably even several times - if he's not done for something more serious first. However Trump is also the kind of megalomaniac who would never even countenance removing himself from office based on such censure, let alone understand its significance.