What is the difference between a random oracle and a probabilistic algorithm?

Question

What is the difference between a random oracle and a probabilistic algorithm?

Answer 1

Essentially a probabilistic algorithm is simply an algorithm that makes random choices (i.e., takes some random bits). So any algorithm that involves sampling random numbers or the like is a probabilistic algorithm.

A random oracle is a theoretical construct mostly used to analyze cryptographic schemes. It is an oracle that on all inputs gives a uniformly random output, but gives the same output each time its queried on the same input. Often this is used as a model of an idealized hash function. There is a more thorough description of it in the answer here.