Relation和Relationship
relation和relationship都是解關係，很多時候可以互通，relationship比較講情感上的關係，relation則比較講工作上的關係。現在分析各個情況：
一、國與國的正式邦交一定用relations，注意這裡一定要用眾數。
Canada and Britain have established diplomatic relations with North Korea.
Britain threatened to break off diplomatic relations with the regime.
但國與國之間的關係則可以用relations（必須用眾數）或relationship（可數名詞），情感上的關係尤其會用relationship。
US-Chinese relations (Oxford Dictionary)
We seek to improve relations between our two countries. (Longman Dictionary)
The Chinese President has said the China will maintain its traditional friendly relationship with Bangladesh（孟加拉）. (COBUILD Dictionary)
the special relationship between Britain and the US (Longman Dictionary)
二、人與人之間的關係既可用relations（必須用眾數）或relationship（可數名詞）。relations通常是指工作上的關係，relationship通常是指情感上的關係。
Relations between workers and management are generally good. (Longman Dictionary)
I have quite a good relationship with my parents. (Longman Dictionary)
She has a close relationship with her daughter. (Longman Dictionary)
三、物與物之間的關係既可用relation（countable and uncountable），也可用relationship（countable and uncountable）。兩個字完全互通。bear no/little relation/relationship to是一個固定片語，解沒有關係/關係不大。
the relation between rainfall and crop yields (Oxford Dictionary)
the relationship between poor housing and health problems (Longman Dictionary)
The fee they are offering bears no relation to the amount of work involved. (Oxford Dictionary)
The lessons bear little relationship to the children's actual needs. (Longman Dictionary)
四、情侶關係用relationship（可數名詞），性關係則是sexual relationship（可數名詞）。情愛的關係不用relation。
She doesn't really want a relationship with me. (Longman Dictionary)
She's had a series of miserable relationships. (Oxford Dictionary)
Are you in a relationship right now? (Longman Dictionary)
He's never had a sexual relationship before. (Longman Dictionary)
五、有血緣關係的人=blood relation/blood relative（可數）
He could be the next-door neighbour, a friend, a blood relation. (Longman Corpus)
六、其他
勞資關係=labour relations/industrial relations
a company with good labour relations (Longman Dictionary)
Nationalization in the transport industries produced neither outstanding industrial relations nor employee commitment. (Longman Corpus)
公共關係=public relations
public relations exercise是固定片語，指改善公關的工作。The project has been disastrous for the bank in terms of public relations. (Longman Dictionary)
Newcastle manager Kevin Keegan looked upon the tournament as a public relations exercise rather than a moneymaking venture. (Longman Corpus)
The tour was considered to have been a successful public relations exercise. (Longman Corpus)
It has been a public relations exercise for this week's by-elections. (Longman Corpus)
種族關係=race relations
We need to do more to promote good race relations. (Longman Dictionary)
Community leaders are working to improve race relations in the city. (Longman Dictionary)
Hawaii has a tradition of good race relations. (Longmae Dictionary)
這三個關係都是用relations（必須用眾數）。