Also when referring to a certain specific sign English speakers use ‘the sign’. The phrase ‘A sign’ is more of a general description used for what it is. “What behind me?” - “It’s a sign.” “Have you seen the turn off yet?” - “No I can’t see the sign.” Hope this helps :)

The difference would depend on how many signs there are which say “Willowsdean”. If there are more than one, you would say ‘a’, unless the context tells you which one. After leaving town, look for a/the sign which says “W…” (‘a’ and ‘the’ are the same here, it doesn’t matter if there are others) Look out for a sign which says “W…”. You can see they have graffiti on them. (all of the signs to Willowsdean have this graffiti. ‘The’ would make no sense here)

There is no difference.

In this case they mean the same