The rapid advancement of generators (e.g., StyleGAN, Midjourney, DALL-E) has produced highly realistic synthetic images, posing significant challenges to digital media authenticity. These generators are typically based on a few core architectural families, primarily Generative Adversarial Networks (GANs) and Diffusion Models (DMs). A critical vulnerability in current forensics is the failure of detectors to achieve cross-generator generalization, especially when crossing architectural boundaries (e.g., from GANs to DMs). We hypothesize that this gap stems from fundamental differences in the artifacts produced by these \textbf{distinct architectures}. In this work, we provide a theoretical analysis explaining how the distinct optimization objectives of the GAN and DM architectures lead to different manifold coverage behaviors. We demonstrate that GANs permit partial coverage, often leading to boundary artifacts, while DMs enforce complete coverage, resulting in over-smoothing patterns. Motivated by this analysis, we propose the \textbf{Tri}archy \textbf{Detect}or (TriDetect), a semi-supervised approach that enhances binary classification by discovering latent architectural patterns within the "fake" class. TriDetect employs balanced cluster assignment via the Sinkhorn-Knopp algorithm and a cross-view consistency mechanism, encouraging the model to learn fundamental architectural distincts. We evaluate our approach on two standard benchmarks and three in-the-wild datasets against 13 baselines to demonstrate its generalization capability to unseen generators.