What is the name of the audio clip used at the start and end of a podcast?

The bit of a podcast at the beginning and usually the very end too with the branding/title+description+jingle that is always the same? Probably the same word describes what is used for the branding of broadcast audio (uh, radio) too. Bookends? Lead-in/outs?

The usual terms I hear are "intro" and "outro". "Intro" is of course short for "introduction", while "outro" is formed by analogy with "intro".

I would suggest that "lead in" / "lead out" as mentioned in your question are probably the most applicable. As Greg suggests, "intro" and "outro" also work, but it's conceivable that you might have a unique intro for a given episode which would be played after the "lead in".

You may even shorten this to simply "lead" for the beginning, and more explicitly use "lead out" when referring to the end.

Just my two cents, but maybe someone in radio or podcasting will offer up an industry accepted alternative.