deliberately & intentionally

As an educated native English speaker, I can tell you that these two words are almost exactly the same in meaning and usage. Most native English speakers would use these two words interchangeably, most of the time.

However, there might be some differences in usage but these might just reflect my own personal usage. "Deliberately" usually represents a malevolent intention but "intentionally" can represent either a malevolent or a neutral or even,(less commonly), a benevolent intention. And "deliberately" is most often used to describe a more immediate and rather simple action, such as, "You deliberately pushed me," while "intentionally" is more often associated with a plan that is more long-term, such as, "I intentionally left the money on the table to see if he would take it." Related to this idea of a plan, the word, "intentionally" is also used when talking about a result of a plan or a cause of an event, such as, "They intentionally planted the false news in the media in order to cause the share price to rise."