The system of having a judge/prosecutor with broad investigative powers is unknown in the US, which is probably a good thing given how the rest of the system is organized.
The jury that hears the evidence in a trial is referred to as the petit jury (small jury). It is convened for a single case.
The grand jury is a standing body (also supposed to be drawn from the populace, and with definite tenure) which hears preliminary evidence and in theory decides whether there is enough of a case that an actual trial would be warranted. It can issue subpoenas (as in this situation).
The rest of the US system is weird. At the federal level the people who judge the cases are a whole branch who do pretty much nothing but that. The actual bringing of the cases is the responsibility of the executive. Oh, various departments of the executive have their own "courts" too that rule with no juries. There is no constitutional reason why this whole apparatus could not be part of the judicial branch but I've not seen any interest in that happening. Actually the executive's courts are pretty clearly not constitutional but they have survived enough challenges that they are simply the way they are.
At the state level the same system is roughly followed but in most, or perhaps all states, the attorneys general (who oversee all prosecutions) and Supreme Court judges are elected. Sheriffs too, which in some states are important police, and even some chiefs of police. You might think that this direct election would reduce the chance of corruption but of course it seems to run the opposite way. The longstanding American distaste for competence is the strongest force against a trained, standing set of people to do things.