The translation issues are addressed well enough in the OP and the comments.
The Latin phrases delegatus non potest delegare and delegata potestas non potest delegari do not have consistently distinct meanings in modern legal usage. Somebody, somewhere may have made a distinction in a case, but this isn't meaningfully uniform across U.S. jurisprudence which is no longer as fond of making fine distinctions between Latin catch phrases as it used to be.
Isn't it the duty, and not a mere task that should be non-delegatable?
Like so many things in the law, there isn't a consistent general answer. The heartland of cases where delegatus non potest delegare and delegata potestas non potest delegari and the English language equivalents of this doctrine historically applied at common law are now governed by a mismash of context specific state statutes which resolve the quoted question differently.
Usually, for example, there are different statutes governing different kinds of court appointed fiduciaries, private entity managers and officers and directors (sometimes with different rules for different types of entities such as a distinction between corporate and LLC officials and general partners in general partnerships in Colorado law), and government officials in different particular types of governmental entities and positions.
The rule isn't even necessarily consistent, for example, between different elected executive branch officials within a single county government. One rule may apply to the county surveyor or coroner, and another to the county treasurer or sheriff.
Even the interpretation of less specific language found in statutes isn't necessarily interpreted terribly consistently from statute to statute within a state, or between states. Largely, the case law hinges upon what context and common sense seems to call for under the circumstances of particular cases.
Also, the common law case law on this question in areas where statutes have not superseded the common law, isn't terribly consistent from state to state, and so far as I know there isn't really any strong regional or historical trend at work. It has been more of a matter of random drift. It is a fine grained enough issue that there isn't a near universal common law rule.
