Adenosine and caffeine are both built on a purine ring system, and that shared scaffold is why they compete for the same site. Adenosine is a purine nucleoside: a purine ring joined to a ribose sugar. Caffeine is a methylxanthine, a purine ring with three methyl groups and no ribose. The ribose is not what anchors adenosine to the A1 or A2A receptor; the purine portion makes the key contacts. Caffeine keeps that purine scaffold and therefore fits into the same orthosteric pocket, the site where the natural ligand normally binds.
What caffeine lacks is the ability to activate the receptor. Adenosine binding changes the receptor's shape enough to engage downstream G-protein signaling; caffeine occupies the pocket but does not produce that activating change. So the structural relationship is: shared scaffold gives access to the pocket, missing chemical features prevent activation. This combination is what makes caffeine an antagonist rather than an agonist.
Because both molecules are competing for one site, the outcome depends on relative concentration and affinity. More caffeine means fewer receptors available to adenosine; more adenosine means caffeine is outcompeted. Neither molecule destroys the other. They simply occupy the same slot, and whichever is present in greater effective amount wins more of the sites at that moment.