In the context of love or partner, it means having established a love relationship based on promises and dedication where a person agrees to continue a life as a couple with the other person. Normally, one person commits to another before getting married, although there are some couples who decide not to marry and remain committed.
A couple’s commitment implies that both people are involved in following certain “rules” so that the love relationship takes place, such as being faithful, not lying, cheating, among others.
In a relationship there does not necessarily have to be any type of commitment or a love relationship, since a relationship can be established with other individuals, such as a family member, a friendship relationship, among others. The relationship itself is a bond or bond that is established with other people in different ways and, therefore, it does not have to be strictly related to something loving, but of any kind.
To give some examples, there are couple relationships where individuals live in the same house, others live in different homes, but all maintain a bond or love relationship.
A relationship can be between different individuals where there is some kind of bond and the commitment is between two or more people who have a love relationship based on promises.