A warehouse schema is the shape you give analytical data once it lands: which tables hold measurements, which hold descriptive context, and how they join. The choice is partly mechanical - star, snowflake, or galaxy - and partly philosophical, because two camps disagree about where modeling should start. Get the shape right and queries are simple and fast; get it wrong and every report fights the structure.
The three table shapes
A star schema puts one central fact table (the measurements - orders, clicks, sensor readings) surrounded by denormalized dimension tables (the context - customer, product, date). It is the workhorse: few joins, simple SQL, fast aggregation. A snowflake schema normalizes those dimensions into sub-tables - product splits into product, category, and department - trading query simplicity for less redundancy. A galaxy schema (fact constellation) has multiple fact tables that share the same dimensions, which is what you grow into once one star isn't enough.
Two philosophies: top-down vs. bottom-up
The deeper question is where to begin. Inmon's Corporate Information Factory builds a normalized 3NF enterprise warehouse first - one integrated source of truth - then feeds dimensional data marts off it. Kimball's dimensional approach goes the other way: build star-schema data marts around business processes one at a time, and tie them together with shared conformed dimensions. Inmon optimizes for integration and consistency up front; Kimball optimizes for speed to first value and business alignment.
How they relate to architecture
These schema decisions sit inside larger structural ones - whether you run a hub-and-spoke architecture or compare an enterprise warehouse against independent data marts. Inmon's CIF is hub-and-spoke by design; Kimball's bus architecture is a federation of marts. The schema you draw and the architecture you deploy are two views of the same set of choices.
Picking an approach
Most teams land on a hybrid: dimensional star schemas at the presentation layer (because that is what BI tools and analysts query well), fed by a more normalized integration layer where source systems disagree and conflicts have to be reconciled. Start with the business process you need to report on, model it as a star, and grow toward a galaxy as more processes share the same dimensions. Reach for full Inmon-style normalization when enterprise-wide integration and auditability outweigh time-to-delivery.