Get going and Get under way

Get going verb - Begin or set in motion.

Get under way and get going are semantically related in start topic. In some cases you can use "Get under way" instead a verb phrase "Get going", when it comes to topics like begin, carry out, come into being.

Get going and get under way are semantically related in begin topic. You can use "Get going" instead a verb "Get under way", if it concerns topics such as carry out, come into being.