What factors affect the threshold voltage in MOSFETs?
Yes, it does. There are two factors at work here. The first is the inherent variability of the manufacturing processes across the surface of the wafer, but that tends to be of concern only over large areas.
The second is called chirality. An example of this in everyday life is having a right hand and a left hand. As a consequence, a glove for the left hand is different from a glove for the right hand.
The source/drain regions are formed by ion implantation into the wafer, after the gate has been deposited. The direction of the ions is not always orthogonal to the surface of the wafer...like rain coming down in a wind. The relatively tall transistor gate material can cause shadows in the deposition, leading to small variations in behavior of the transistors.
Also, the etch of the gate electrode may not be exactly uniform in all directions.
So, if you want two transistors to be matched, use exactly the same size and shape for them. Orient their gates in the same direction. Use the same side of the gate (left/right or top/bottom) to be the drain for the transistor. Keep the transistors close together.