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The term “sparsity” is widely used in high-dimensional materials design, yet its meaning remains conceptually unstable and methodologically consequential. This article argues that sparsity in materials discovery should not be treated as a single condition, because the challenges faced by active-learning systems arise from qualitatively different sources. A boundary framework is introduced that distinguishes data sparsity, representation sparsity, and coverage sparsity, and relates each to a distinct failure mode in surrogate modeling and acquisition design. Data sparsity describes the imbalance between the number of evaluated materials and the effective volume of the design space; representation sparsity concerns zero-dominated descriptors; coverage sparsity captures the uneven spatial distribution of samples across composition or descriptor space. By separating these regimes, the analysis shows why standard acquisition functions often underperform in realistic campaigns: they assume sufficient support for interpolation, manageable descriptor structure, and reasonably uniform sampling. The article formulates operational criteria for diagnosing each sparsity type and demonstrates how strategy selection should change as the dominant constraint shifts. In doing so, it provides a clearer vocabulary for high-dimensional materials design and a practical basis for more reliable, sparsity-aware active-learning workflows.