This answer is based off of my experience living in the UK for all my life.
In my experience "correspondent" would usually be used to refer to someone who is more knowledgeable about a specific topic, normally because they specialise in the story's specific field. For example, a news organisation may have a technology correspondent, an education correspondent, a politics correspondent, etc.
Reporters, on the other hand, generally refer to "normal" journalists who do not specialise in the specific field. Reporters are usually at the location of a news story, or are following it closely another way (e.g. online) and report the facts.
In many situations, you might have a reporter at the location of a news story. They may be interviewing people for the story, compiling information and facts about the story, and tracking the most recent developments. All of this would then be relayed to the main newsroom where a correspondent may then answer specific hypothetical or real questions about the story based on this information.
For example, in the case of large floods, you will often have a reporter at the scene of the floods, interviewing people about their experience with the floods and how it has affected them, as well as finding out specifics from emergency services and officials.
This information gathered will usually be sent back to the reporter's headquarters or central news room, where they can then have an environmental or flooding correspondent answer specific questions, such as "Will the flood levels continue increasing?", as an example.