What is the difference between normalization and standardization in machine learning?

I'm learning data preprocessing in machine learning and often come across the terms normalization and standardization. I understand that both techniques are used to scale numerical data, but I'm confused about how they differ and when each one should be used.

Can someone explain the difference between normalization and standardization, how each method transforms data, and which machine learning algorithms benefit the most from each approach? A simple example comparing the two techniques would also be very helpful.