That's a question with a whole lot of aspects.

I think of a potting shed as a fairly open structure; three sided or half walled with a lattice roof or (at a minimum) not toally enclosed. I built my dw a "potting shed" that consists of a roof supported over a pavered covered area with sink, benches and shelves, that is totally open to the elements, supported by eight 4x4 posts

Bottom line; a potting shed is usually open to some degree to the ambient weather conditions (temp , humidity etc) whereas a greeenhouse is a much more controlled environment.

You can , of course, pot in a gh,though once you build one you'll quickly cherish whatever space you have and move basic "potting" outside.

You can grow orchids outside in a "potting shed area" in my area of CA during the summer but you can't leave them out there past about mid Oct.

You can readily repot large house plants in a potting shed in the middle of Summer but you probably dont' want to drag the them into the gh to do that simple task.

You can start seed in flats in a potting shed but, without control of the temp and humidity, you'll have to wait longer into the year (depending of course on your zone) or limit the kinds of plants you can start.

That's a start on the question anyway.

My idea of a potting shed is a structure in proximity to a greenhouse that has a conventional roof and limited natural light penetration. When greenhouse temperatures are in the 80s or higher you want to be potting and doing other tasks in the shade. And the materials at your disposal don't need the greenhouse light or humidity.

Many people do limited potting tasks in the greenhouses if room permits, but as Clavero said the space is more at a premium in the greenhouse because of the environment it creates for plant growth.

Two good answers.

I have a potting bench alongside our storage shed, just outside the greenhouse door and that's what I use in fair weather. I use an area of one of the greenhouse benches in cold or rainy weather. Most of the potting supplies are kept on the enclosed lower shelf of the outdoor potting bench, so they're handy for both locations.

BTW, in need of a potting tray to use inside the greenhouse, I grabbed the top of a large Rubbermaid container and flipped it over - it has worked out so well I've decided to stick with that instead of buying an authentic 'potting tray'.

I have a potting area inside my 10x16 greenhouse-an old kitchen counter unit that has been retrofitted with a sliding bin under the sink to store soil in. It provides lots of drawer and cupboard storage and 4 feet of counter space too. In more northern climates, (I see you're in zone 5) you'll appreciate having the potting area inside the building on windy, rainy and winter or early spring days and on nice days you can open the doors and venting. We built a small shed behind the greenhouse to store extra pots, bags of ProMix, perlite, tools etc. in.
Having said that, I also have an open air potting area beside my greenhouse-a bench table with an antique sink in it. It's nice for really messy jobs and can be used in good weather.

Here is a link that might be useful: Greenhouse and Potting Area