C

Step 1: Let's analyze the assertion. The assertion states that if the sum of two unit vectors is also a unit vector, then the magnitude of their difference is \(\sqrt{3}\).
Step 2: For two unit vectors \(\mathbf{a}\) and \(\mathbf{b}\), we have:
1. Their sum is \(\mathbf{a} + \mathbf{b}\). If this is a unit vector, then: \[ ||\mathbf{a} + \mathbf{b}||^2 = 1 \]
This can be expanded using the dot product:
\[ ||\mathbf{a}||^2 + ||\mathbf{b}||^2 + 2 \mathbf{a} \cdot \mathbf{b} = 1 \]
Since \(||\mathbf{a}|| = ||\mathbf{b}|| = 1\), this reduces to:
\[ 1 + 1 + 2 \mathbf{a} \cdot \mathbf{b} = 1 \]
\[ 2 + 2 \mathbf{a} \cdot \mathbf{b} = 1 \]
Hence, \(\mathbf{a} \cdot \mathbf{b} = -\frac{1}{2}\), which means the angle between the vectors is \(120^{\circ}\).
Step 3: Now calculating the magnitude of their difference: \(\mathbf{a} - \mathbf{b}\):
\[ ||\mathbf{a} - \mathbf{b}||^2 = ||\mathbf{a}||^2 + ||\mathbf{b}||^2 - 2 \mathbf{a} \cdot \mathbf{b} \]
Thus,
\[ ||\mathbf{a} - \mathbf{b}||^2 = 1 + 1 + 1 = 3 \]
Therefore, \(||\mathbf{a} - \mathbf{b}|| = \sqrt{3}\), making the assertion true.

Step 4: Now, let's analyze the reason. The reason states that we use the square law to find the resultant of two vectors, which is a general statement about vector addition. While it's true, it's not the reason why the assertion holds in this specific case.
Therefore, we conclude that the assertion is true, but the reason is false.
Hence, the correct choice is C.