"My perception is my reality" would be an acceptable way to put it, but "perception is reality" is simply not accurate.
"My reality" is not equal to reality, it is less than. "My reality" encompasses only one angle in, to a vaster reality. Each of us has a self - our angle in. And for each of us, our perception is indeed all we know! But there are glimpses we catch, the keen glare of our own observation reveals views of others' angles into reality, where they intersect our own. These glimpses and views give compelling cause to suppose that others exist, and that each of those others has their own experience of reality, and to further suppose (because we can only be so egotistical) that their experience is comparable in weight and validity to ours.
Even though we may disagree royally on interpretation! Interpretation is a purely internal matter. Interpretation does not claim to affect reality, it seeks to "get" it. To hold in the mind a description of reality that makes sense. And one's interpretation it is funded and fueled by the foods for thought that all others provide.
Once we go in for the idea that your "my reality", my "my reality", and the "my reality" of others are all comparable in validity, where do these realities intersect?
Reality, without qualification or presumption of attributes. We apply attributes liberally within our own slice: my reality may be sad and little, but if so, it is only because I have a sad, little reality. Reality, unqualified by possessives or further descriptors. Reality, which is not mine and which is not yours - though we each have our own share of it.
And each of our shares in it is vast. And each of our sovereign shares overlaps greatly with the shares of others! Reality, which we cannot comprehend or plumb, except fully - within the extent that our grasp can reach. Reality, which is the thing we must agree upon, for it to make the same sense to both of us. Reality, upon which it is not necessary to agree! None of us need agree upon reality's nature or extent, because however much a suddenly-shared grasp may turn my reality upside down, reality itself is not rocked by that epiphany.
Reality is not changed by our agreement or disagreement about it, or within it.
There is only one of these. Or at least, I'll let Billy Occam have his say on that one. There certainly does appear to be only one of these.
Anyone who truly believes perception equals reality; anyone who believes their "my reality" is equal to reality - be very careful and respectful of those people! Their viewpoint is just as valid as yours. It's called psychosis.