The little word up is the whole picture. Think of filled up, topped up, warmed up: up means poured in until it reaches the brim. Someone who is loved-up is not just in love, they are full of it, and it is running over the edge into how they look — the smiling, the photos, the arm that will not come off a shoulder. The two uses differ only in where all that overflow is pointed: at one person, or at a whole room of strangers.
Two branches
滿出來給一個人
愛滿到藏不住，而且全部朝著同一個人去，所以旁人一眼就看得出來。
adjective · C1
Full of romantic love for someone, and showing it — the way a couple looks when they cannot stop smiling at each other. It is a light, informal word, used much more in British English, and very often about how a couple looks in photos.
熱戀中的
滿出來給整個場子
同樣是滿到溢出來，只是不再對準一個人，而是朝全場散開，連不認識的人都算在內。
adjective · C1
Feeling warm and full of love towards everyone around you, not towards one person. In British slang this is said about people at a club or a festival who are in that state because they have taken the illegal drug ecstasy (MDMA).
（對誰都）愛意滿滿的