Most of their differences are differences of emphasis.
Mnuchin is drawing the issue narrowly: the particular technologies called "Artificial Intelligence taking over American jobs". And he is, at least as I read him, is elliptically criticizing high stock market values for "unicorns": companies with valuations above a billion dollars and yet no past record or clear future path to producing revenues to justify such valuations.
Summers is drawing the issue broadly: "the... impact of technology on jobs". And he points to valuations for the proven and highly profitable tech giants Google and Apple that seem no more than fair. I think that Summers is right on the rhetoric--a Treasury Secretary cannot answer questions narrowly, for even his most careful and narrowest answers will be heard to have broad implications. How to handle the coming of information technology is a major issue. Discouraging investment in high tech is not wise from society's point of view.
Yet I have great sympathy for what Mnuchin is trying to do as well.
He is warning investors that, while great technologies are certainly worth investing in from society's point of view, the path to sustained profitability is a difficult one, and non-experts should not routinely invest in castles in the air. And a Treasury Secretary has enough other issues--or perhaps different aspects of the same issue--on his plate that it is a distraction for him to fear the rise of the machines.
In fact, let me lay down a marker: to conceptualized the important issues in a way that leads us to fear robots, as "Artificial Intelligence taking American jobs", is profoundly unhelpful. There are better places to put the focus that are more likely to lead to constructive action.
Start from the premise that it is quite difficult, in theory, to design self consistent economic scenarios in which (a) the government is properly doing its job to stave off demand-shortfall depression and (b) the workings of a market economy inevitably lead to technological progress impoverishing unskilled workers. (You can do this if the true sources of value are critical and scarce natural resources--but that is the agrarian-epoch middle ages, where what is scarce and valuable our plots of good agricultural land and the spears to defend them, not any modern industrial or post-industrial civilization.)
When the true sources of value are either of the work of human hands or the work of things human hands have made--well, Karl Marx could never make his theory self-consistent. There was always a big South-Park underpants-gnomes gap in the middle between technological progress and unskilled worker impoverishment. And Marx was the smartest and most dedicated of those who have tried.
Technological progress makes what is produced primarily by machines (with relatively lesser contributions from unskilled workers) more useful. But that by itself does not impoverish anyone. In order for the process to impoverish unskilled workers, technological progress also has to make what is produced primarily by unskilled workers (with relatively lesser contributions from machines) less useful. And it is very hard to see how that can be the case. What keeps the relatively cheap machines used by unskilled workers in labor-intensive occupations from becoming more powerful and so amplifying the powers of workers employed in those sectors to make useful things? It is possible, as Paul Krugman and Ryan Avent have argued. But it would have to be a very odd set of technologies indeed.
Thus the historical cases in which the workings of a market economy has led technological progress to impoverish unskilled workers turn out of be relatively few. The rise of the machines has to make the value of the useful things produced in the labor-intensive sector fall rapidly and sharply. Machines have to increase production so much that potential consumers become satiated and are no longer willing to pay for the products made by unskilled labor that they were happy to pay for before. The handloom weavers of 18th and 19th century India and Britain become the canonical example. Machines made exactly what they made, and made it at massive scale. Because of limited demand the value of what the handloom weavers made fell massively, without corresponding price declines in the commodities that handloom weavers bought.
From this perspective the coming of the robots and the rise of the machines are not a danger to be feared and a process to be halted. From this perspective our problems are, almost exclusively, problems of social engineering and of maintaining a fair balance of relative incomes. The tasks of society become threefold:
Make sure the government does its proper macroeconomic job so that the market can work: maintain full employment via a high-pressure low-unemployment economy.
Redistribute wealth to maintain a proper distribution of income so that the societal well-being function that the market economy understood as a social calculating engine seeks to maximize is in fact a function that corresponds to our values and morals.
Educate and train workers so that they can use advancing high tech tools to increase their powers to make useful things, even or perhaps especially in labor-intensive industries.
Fear of "Artificial Intelligence taking American jobs" does not help direct attention toward coherent and helpful policies to attain any of those goals. Thus it should not be on a Treasury Secretary's radar screen.