I was wondering if to annoy and to bother are synonyms, or if there could be a difference in meaning.
The word bother can be used in these patterns:
These mean: to make an effort or suffer a small inconvenience to do something; and not to suffer the inconvenience to do something. Usually the first, positive, form is used in questions, or conditionals rather than plain statements:
The verb "annoy" cannot be used in the above ways. You cannot "annoy to [verb]"; it is not grammatical, because "to annoy" does not take a verb complement.
To be bothered has these meanings:
To be annoyed only means this: to be slightly angry. To be extremely annoyed is tantamount to being angry. Annoyance is a reaction like anger, but much more mild. It is a negative emotional reaction to a thing or situation, accompanied by a wish that the situation or thing were different, or didn't exist, or at least didn't exist at the same time and place as the one who feels annoyed.
So as you can see "to bother" has many meanings, one of which is a synonym of "to annoy", and so "to annoy" cannot generally be used in place "to bother"; only when the meaning of "to bother" is "to cause a displeasure, like a slight anger".
On the other hand, substituting "to bother" in the place of "to annoy" can result in a loss of clarity, because the meaning of "to annoy" is narrower and more specific. For instance "what she said annoys me" loses its specific meaning if reworded as "what she said bothers me"; context may not be sufficient to recover the proper meaning.
Both words can be interchangeable at times but there are nuances in meaning that will lead to the choice of the one or the other in some contexts. I feel "annoy" expresses more displeasure at something or someone.
If something is annoying me, I feel angry or distressed. "That bird was annoying me with its early morning chirps, I took a gun and got rid of it."
If something is bothering me, I feel worried or irritated about it. "My mum keeps bothering me about tidying my room."
In the negative they're not interchangeable most of the times.
But "don't annoy your little brother" and "don't bother your little brother" sound pretty much the same to me in meaning.
"Bother" is more general than annoy and means "cause to feel a negative emotion or sensation."
For instance, if I am scared of flying, I might say that turbulence really bothers me (it makes me frightened). "Annoy" does not work here. Or I could say "onions bother my stomach" to mean they make me sick; again, "annoy" doesn't work.
In general, "annoying" refers to a non-serious type of bothering, e.g. a house flies' buzz annoys you, or siblings annoy each other.
Yes they both are similar in meaning, but not in some cases where bother is used to mean someone is made to feel worried and annoy can't fit for the same.
Also, Bother is an exclamation of annoyance and used as an interjection too.