I believe what you're after is NIST's Quantum ZooNIST's Quantum Zoo, a comprehensive catalog of quantum algorithms maintained by Stephen Jordan. Its sections include:
- Algebraic and Number Theoretic Algorithms (14 items)
- Oracular Algorithms (34 items)
- Approximation and Simulation Algorithms (12 items)
https://math.nist.gov/quantum/zoo/ and for each algorithm it includes its speedup, a description and relevant references. The third category would be the answer to the present question.