Except due to the meager energy returns of photosynthesis, complex plants sacrifice almost all their ability to move to maximize their returns from photosynthesis, becoming even more static with size.
Animals, however, can move to collect compounds and being able to move allows them to profit off of moving themselves (requiring lots of power, or energy over time). A human walking is about 87 Watts (joules/second or mass*speed), which is about the power cost of a good flourescent bulb. The energy produced by power plants is much greater than eating things, though. Adding on such things as metabolism or complex nervous systems, and the cost increases. Photosynthesis just doesn’t provide that much power.
There are motile plants, most notably euglenids and dinoflagellate alga. However, these are all unicellular, with sitting and waiting simply being more efficient at larger sizes for photosynthesizing. Note that while surface area increases quartically (a^2) with increasing radius, volume increases cubically (a^3), so large plants don’t have much energy to waste moving their cubically-increasing mass. But if they want more surface area, they’re going to have to increase their volume until they get the precision necessary to form leaves (which are thousands of cells thick).
You’re right about there not being “plants” and “animals,” instead we have “aitjhas” and “tyaqs.”
By that you mean having xylem/phloem, but no photosynthetic tissue? Then you aren’t really a plant, just plant-like. [insert image of person raising finger, then bending it]