What do you call a "non-probabilistic Bloom Filter"?
This is related to the notion of "fast path, slow path" from computer systems.  In systems, one common optimization method is: if there is a common case that can be handled fast and is common, first test whether the input falls into that case and if so solve it and return immediately; otherwise, fall back to the complex computation.  For instance, the slow path might have to handle corner cases and difficult situations that arise only rarely.