People often confuse these two terms. Actually the difference between bragging and inspiring others is something that depends on the observer's mind.
The bitter truth is most people do not become happy seeing your success. Beacuse most people are not successful. When you are in a position where they could not be it doesnot make most people happy. From jealousy, generates frustation. That's when they try to defame you. And they console themselves saying that you are bragging.
Of course if someone uses arrogance while talking about his accomplishments then it is showoff and it is just because they are not mature enough for their success. But there are good people who talk about achievements to more people so that others can also achieve something in their own field. Comfusing this with bragging really make those good people feel bad.
So the next time someone throws shade at someone saying that they are bragging about something, just think properly that is it really bragging or they are just manipulatin.
@Telesfor sir I would be really happy if you read this article. Hope you will like it.