Should I make fake conceptual projects to build up work for a portfolio? Or, should my portfolio just be artwork in various mediums?

There's literally no difference between those two things. Knock yourself out. After all,  the large majority of us provide design services only, not construction. 

Hate to break it to you buy anywhere from 30-90% of the stuff you work on as a professional will never be built. So yeah, just make some shit up.

it’ll be harder than you think to do fake.

All of my projects in my portfolio were design exercises I gave myself

1 - a chair

2 - a pavilion from 3 solids

3 - a 1 story 1000sf house in the woods 

4 - Mobius strip Cartesian plane box

I made sketches, diagrams, drawings, renderings, and physical models. 

I think the wording gives it a negative connotation.

You are presenting your own designs and ideas, those are not fake.

Whether you actually worked on a design exercise at school, or a professional setting, or you gave yourself a design exercise to work on, it's still not fake.

Whether it's built or not, still doesn't make your design idea fake. 

The only time it's fake is if it's not your work and you presented the work as your own, aka plagiarism and intellectual property theft. 

Self-generated and theoretical projects are not 'fake" when honestly and clearly presented as such.  "Fake" work would be something that has an element of dishonesty in it.  An example of this would be claiming that your designs were done for paying clients and they really were not. 

KingsMake, almost all the projects in a school you are trying to get in are "Fake Projects". Just so you know...

Do competitions, but not entering them. Hold yourself to the same schedule and same constraints, that way results will show process and intentionality.

I do that for fun in my spare time.

Thank you all for the advice. I think using the word "fake" in the title wasn't a great choice. I meant like making up my own prompt and criteria at home. I thought admissions would be like "Why did he do this?"

A starting point might observation and critical thinking about designed landscapes you use locally or have visited in other places.   Document it with photography, graphics, and some short text.  

Never do fake projects, you might work somewhere where this is the norm but it is a poor place to work, they might make candlesticks and plastic furniture.

I came across an ad for a design firm in magazine that had been dropped off at the office.  Saw the ad,  liked the design for a "proposed house" which a presumed was in a community I know, so I checked out his website to to see if I could find the exact location of the build.

The said "design group" was a picture of one guy who looked like a posing porn star, who had all these proposed homes all over north america, but not one built project.

I am now convinced all the design are AI generated and the who website is false. Crazy, but is that where the profession is going.  Haha time to retire.....or update my website ( oh yeah, I don't have one )

“Fake” projects are the most important way to develop your skills.  If you rely on paid work only to develop your skills, then your progress is reliant on others.  It’s important to have a space to learn and play in that is separate and independent.  The key to doing these projects is to either come up with a basic generic condition - and then to find a multiplicity of ways to organize space, or to find specific local spaces that you feel can be improved and then devise solutions, like a neglected park or vacant lot. Keep it as diagrammatic as possible.  Start to identify language and strategies in these explorations.  It’s better not to pass this off as some kind of “real” thing.  Instead, embrace the diagrammatic nature of it.   Think of it as if the intention is to create a study of spatial language and order.  It’s a study, not a “fake” project.