Please tell me the difference in meanings of the words 'issue' and 'matter' by giving some examples.
Issue and matter are considered synonyms, and, indeed, they are very similar.
According to Merriam-Webster:
a matter that is in dispute between two or more parties b (1) : a vital or unsettled matter <economic issues> (2) : CONCERN, PROBLEM <I have issues with his behavior> c : the point at which an unsettled matter is ready for a decision <brought the matter to an issue>
1 a : a subject under consideration b : a subject of disagreement or litigation c plural : the events or circumstances of a particular situation d : the subject or substance of a discourse or writing e : something of an indicated kind or having to do with an indicated field or situation <this is a serious matter> <as a matter of policy> <matters of faith>