Let's get started! or let's get going?

Solution 1:

It seems that the similarity of your two phrases hinges on the choice of what my grade-school English teacher called "the vulgar verb", namely get. Thus the crux of what's being said is much the same, because the principal verb in each sentence is one and the same, calling simply for a change of state. However, "go" and "start" are neither synonymous nor interchangeable. Each of these verbs carries its own particular nuance, which is to say that there is clearly a difference between "Let's start" and "Let's go" and that it is ultimately this difference that colors one's understanding of "Let's get started" and "Let's get going."

For example, in the context of beginning a game of cards, "Let's start" sounds natural enough but "Let's go" begins to sound impatient. Now consider "I must (have to) go" versus "I must (have to) be going" and you begin to see the effect of the present participle's use, with "going" suggesting that I should have left already. Similarly, "Let's get going" suggest that time is a-wasting, while "Let's get started" does not.