The post-Jon Stewart version of “The Daily Show” that Trevor Noah and Comedy Central unveiled on Monday night was a bit like a new iPhone.

If Mr. Noah plans to overhaul “The Daily Show,” we have yet to see it.

T were segments on the departing House speaker, John A. Boehner, and the discovery of signs of water on Mars.In fact – in an opening that veered dangerously close, for a comedy show, to fear – Mr. Noah framed his occupation as widening Mr. Stewart’s work.

Referring to the last host’s goodbye desk bit, Mr. Noah said he hoped to “Continue” the show’s battle against phoniness.

A bit with the correspondent Jordan Klepper theorizing on Mr. Boehner’s replacement became a meta-commentary on Mr. Stewart’s replacement, including the buzzwords that have been floated to describe how Mr. Noah’s show might be different: “I just keep hearing ‘global’!” Mr. Klepper said.

A back-and-forth with all the new correspondent Roy Wood Jr. about the chances of black people colonizing Mars emphasized Mr. Noah’s readiness to handle race, an acknowledged past blind spot of the show.

Fine: It Is by researching his differences – and sometimes by getting in trouble or disappointing Mr. Stewart’s loyalists – that Mr. Noah will need to find his own “Daily Show” voice.