As BioBrains says, it is usually assumed that the last author is the author who has overall responsibility for the publication, usually the head of the research group, grant holder, or line manager. The research would usually have been their idea in the first place. They are the person with whom the buck stops if there is something wrong with the paper. (If my student or postdoc publishes fraudulent data, both they and I get in trouble, if the fraud is on my part, then only I get in trouble). This is sometimes known as the "senior author".
In theory, the corresponding author is the person who is mostly likely to be in a position to answer , or find the answer to any (and I mean any) question about the research. Even if its 10 years later.
Some people will use corresponding to try to indicate that either more than one person should be regarded as the senior author, or that the person last on the list is not the senior author (if, for example the first author should be regarded as both the first and senior author). We often use it very much like "* these authors contributed equally", but for joint last authorship, rather than joint first, particularly where multiple fields are involved, and there is unlikely to be one person who knows about everything, or has overall responsiblity. The extent to which people recognise/acknowledge/account for this is variable.