Is it same as "having a better relationship with" ?
I do not think the arena's architecture should relate better to the context.
This frees their imaginative capacities, and lets them relate better to the world around them.
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In terms of usage: no. “Relates better” is used for comparative similarity, whereas “having a better relationship” implies a bond comparison between entities.
The word “relate” is a similarity measure. When paired with better, it provides a similarity comparison between three entities ex. given A, B, and C, stating that B relates beyter to C implies that B is more similar to C than it is to A. By contrast, a relationship does not imply similarity, but rather a bond or connection of some kind between B and C. Bonds may be compared, but when compared, suggest the quality of the bond rather than the entity itself.
To distinguish the two, it is useful to consider the kind of qualities at play. Relates better relies on intrinsic qualities of B and C for the similarity measure, whereas having a better relationship relies on extrinsic qualities, such as some sort of joint object, action and/or shared experiences.