Sorry
Use for more serious apologies or to express sympathy for bad news. It's stronger than 'perdón' and means 'I feel it.'
A casual 'sorry' or 'excuse me' for minor things, like interrupting a friend. Use with people you address as 'tú' (informal 'you').
The formal version of 'Disculpa.' Use it to apologize to or get the attention of strangers, older people, or in professional settings (anyone you'd call 'usted').
Sorry! I accidentally stepped on your foot.
I'm sorry, I can't go to the party.
Excuse me/Sorry, do you know what time it is?
Excuse me, sir, you dropped your wallet.
I'm very sorry about your grandmother.
The distinction between 'perdón' (for a mistake), 'lo siento' (for sympathy/bigger issues), and 'disculpa/e' (to get attention/minor apology) is understood across the Spanish-speaking world.
You will frequently hear 'Qué pena contigo' or just 'Qué pena' used to mean 'I'm so sorry' or 'My apologies,' especially for inconveniences. For example, 'Qué pena la demora' (Sorry for the delay).
Because they use 'vos' instead of 'tú', the informal command changes from 'disculpa' to 'disculpame'. The meaning is exactly the same.
The use of 'lo siento' is more strictly reserved for expressing condolences. For apologizing for your own actions, 'perdón' is almost always preferred. You will also hear 'perdonad' and 'disculpad' for the plural 'vosotros'.
Using 'lo siento' for small things. Saying 'lo siento' when you bump into someone is too dramatic. Use 'perdón' instead. 'Lo siento' is for when you hear someone's dog died, not when you take the last piece of cake.
Confusing 'perdón' with 'con permiso'. 'Perdón' is an apology for something you've already done (like bumping into someone). 'Con permiso' is what you say *before* you do something that might inconvenience them (like trying to get past them in a crowd).
Mixing up 'disculpa' and 'disculpe'. Using the informal 'disculpa' with an older person or a police officer can sound a bit rude. When in doubt, using the formal 'disculpe' is always the safer and more respectful option.