First, for Ito processes and Brownian motion. Ito process is a continuous-time trajectory with random evolution, so non-smooth and very kinky - also has a fractal look: no matter how much you'd zoom in, it will look similar. Ito process consists in fact of two parts: the drift part (deterministic evolution) and the diffusion part (where all the kinkiness and fractalness comes from). If Ito process does not posses the latter, it just looks like a continuous smooth trajectory. For example, $y = x^2$ is such an (purely drift) Ito process. In contrast, if Ito process has only diffusion component, you won't be able to spot it. That is, when the diffusion component is present, it's hard to say whether there is a drift component or not, because of the noise diffusion provides.
Brownian motion is a special case of an Ito process, and is the main building block for the diffusion component. In fact, any diffusion is just a time scaled Brownian motion. One important property of Brownian motion is that its increments are uncorrelated (in fact, they are independent) whereas in general Ito process there can be loads of cross-correlation happening.
Finally, formally random walk is a discrete-time process - hence not comparable with Ito processes which are continuous-time things. On the other hand, random walk must also have independent increments - that's why Brownian motion sometimes referred to as a (continuous-time) random walk.