When to use Entschuldigung vs. Es tut mir Leid?

Which word is appropriate to use if you make a mistake? For example, we say 'I'm sorry' most of the time...if we've miscounted change, spilled a drink on someone, gave someone the wrong directions, or wasn't listening to what someone was saying...we usually wouldn't say 'excuse me'... show more Which word is appropriate to use if you make a mistake? For example, we say 'I'm sorry' most of the time...if we've miscounted change, spilled a drink on someone, gave someone the wrong directions, or wasn't listening to what someone was saying...we usually wouldn't say 'excuse me' for these actions. Are the meanings derived the same with these German words? I rarely hear 'es tut mir Leid' so, do German-speakers mostly use 'Entschuldigung' for both 'excuse me' and 'I'm sorry'? Is 'es tut mir Leid' for more serious actions like someone's pet dies (for example)?
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