gist is a little informal, summary is more formal.
To me, the gist of something is probably shorter than a summary.
You can say 'in summary, xxx', but you can't say 'in gist'.
You can 'Somebody's summary' but you can't say ' Somebody's gist'.
In fact, I suspect you can only say 'the gist'.
"I couldn't get the gist of what she was saying".
"The gist of it is that he was lying all along".
"In summary, the planet really does have a gaseous core, and a magnetic dipole".
"My summary of her work will be published later this month".
"The summary he wrote is a little hard to follow in places".