The English language words Connection, Relation and Relationship have similar meanings, but they are different, as I shall explain, using British English examples.
Connection is a noun (connect is the verb) and means the fact of two or more things being together - physically or in concept.
"I connected the speakers to my television."
"The detective will connect the clues to identify the criminal."
"The wires are used to connect different ports."
Relation is a noun (relate is the verb) and means the ways that two or more things are connected. It is used when describing ways in which two things are similar or different.
"The relation between poverty and low life expectancy is very clear."
"Inflation is highly related to growth in incomes."
"I see no relation between my gender and whether I should be allowed to enter the competition."
"Relations between the countries in the United Kingdom are very strong."
Relationship is also a noun and also describes the ways that two or more things are connected, but more emphasises the state of being connected. We often talk about people being in relationships, as lovers, or close friends. So, relation emphasises more the ways in which things are connected, and relationship emphasises more the fact and reality of being connected.
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