Then do we say that there is an relationship between the two variables, or there is an association between the two variables,

Relationship is synonymous with correlation and denotes the strength and direction  of interdependence between quantitative variables. Association merely implies that variables are dependent on one another but the strength and direction are unknown.

relationship determines cause and effect between two variables but association just shows any correlation between variables.  relationship is assessed through regression and association is assessed during correlation. Is that true ? TQ.

No, relationship and association are virtually synonymous.  Both words express the idea that at least two quantitatively measured variables covary.  The value of one is connected in some way to the value of the other.  Correlation allows you to assess the statistical significance and strength of this association (or relationship), as well as whether the association is direct or inverse.  Regression is a special case of correlation that allows you to not only assess what correlation assesses, but to make predictions about what the value of a "dependent" variable will be based on the value of an "independent" variable.  (The reason I have used quotation marks is to indicate that specifying certain variables as independent in a regression equation, and others as dependent, does not necessarily reflect a cause and effect relationship.)  For example, if I know that a value of x on GRE is predictive of a value of y on graduate school GPA, that could be quite valuable information, but it does not clearly and unequivocally establish that GRE scores cause graduate GPA.

Association is  merely referred to any relationship between measured quantities (variables), whereas,  Relationship goes on further to indicate the direction of the association ( if positive or negative association), the form of the association( if linear or non linear), and also the strength of the association if weak, moderate or strong. Hence, two variables are known to have a statistical relationship if we can predict the second variable  from the value of the first variable provided.

Association is assessed by Correlation since Correlation is a measure of association between two variables if the association is positive, negative or no association.

Relationship is assessed by Regression  to predict the dependent variable when the independent variable is known as it has prediction capability.

Can this be applied to a case of two tests measuring the same thing. Test A measures variable 1 and test Bmeasures variable 1. Can we measure the relationship of the two tests or is there a better statistical tool for such measure?

both are same.

Association and relationship are not yet statistically measured, but could be seen the prone of the direction, form and strength. Correlation is biimplicative and regression is implicative. The later discribe cause-effect or independent-dependent variables.

association indicates a relationship which is not specifically showing the nature or direction where as a relationship usually measured through correlation coefficient is directional and may be +ve, -ve or non-directional

https://www.theanalysisfactor.com/the-difference-between-association-and-correlation/

Relationship indicates the link among or between variables. It also tells us what kind of relationship i.e., positive or negative. And it can probably use to regress the effect of the relationships as well.

Association is simply the link between variables regardless of positive and negative.

I'm not statistician. Based on my understanding, relationship refers to the measure of the linear relationship of the variables between -1 to 1 and 0 that indicates no relationship whereas association refers to any relationship between the variables whether linear or non linear. I will be thankful for any reply to this.

Association doesn't indicate the directionality whereas relationship shows the strength and direction of variables- positive or negative. Chi-square test can be used to find out the association and Correlation tests can show the relationship of the variables (+/-), provided that the assumptions required for the tests are met.

I don't think there is a clear difference. If authors choose to use both words within a document then they should probably be careful to define what the difference is in meaning. In most cases I suspect there may be little benefit to using both terms.

x variable and y variable, if the association is implicative, the coefficient becomes regression, and if biimplicative, the coefficient is known as correlation coefficient (r). Association is nonparametric of correlation, and relation is nonparametric of regression. There could be negative or positive (direction), linear or nonlinear. And the straightness is near 1 is the powerful association or relation.

Difference between Association and Relationship

i) Both are known with at least two variables

ii)both may indicate the direction of the relationship( if positive or negative association) measured by Covariance

iii) both have strength and are measured by correlation coefficient that can indicate weak, moderate and strong

iv) However, relationship indicate form, either linear or non-linear

v) Again, in relationship, one of the variables involved in the relationship (independent variable) may or may not have statistical power to predict the second variable(dependent variable), a causal relationship.

While two variables associating may have no causal relationship or artificial linearity as many are computed using ranks.