Sealer is used to stop the ink rubbing off or smudging and goes all over the printed area. Varnish is a gloss or matt coating (like a perfectly transparent ink) that can be printed in shapes or blocks to highlight items on the page.
It is quite common to add a sealer if the job is to be run through the press again, for instance to put on a varnish.
We will on occasion "seal" the sheet before putting the color down to get the paper to more readily accept the ink.
We had a job last week printing on some weird pearl colored coated paper. The pms ink wouldn't stick so we had to put a varnish sealer down first so the pms ink would adhere to the paper.
Thank you both.
We call ''varnish'' glossy or mat,the transparent ink that protects printing process ink from scratching-especially in jobs with heavy TAC-.
If it's applied in certain blocks-or headers or whatever,then we call it spot varnish.
Both of them are done on press.
Next comes lamination.
A plastic transparent layer on top of the print job,be it mat or gloss done in a laminating machine-don't know how else can i put in English.
If it's done topically,to emphasize a picture or a picture element,or some letters for example,then we call it spot uv.
A usual one is for a cover to be mat laminated,with glossy spot uv on the brand logo.
So most probably,the client refers to varnish as ''sealer''-as i first thought- and to lamination as varnish-which didn't crossed my mind until i red StudioMonkey's answer.
I thing we'd better contact the client!
Thank's again!
ps The biggest -by far- problem on printing,(and to every other industry i guess) is good,clear and precise communication.
If on top of that you ad the different slung of printers and designers,then things may come even trickier.
If you're lucky enough,maybe you'll even have the chance to combine all of the above with the different native lanquages of customer,agency and printer!

ps2 In printplanet someone replied it's aqueous coating.That should be the most logical explanation-taking in mind that text needs
offset sealer and cover needs
offset varinsh