The Heart represents love and romantic relationships in general, passions and a Querent’s love life. It also represents caring and altruism, so is quite a deep and pure card to do with a person’s experience of love and the core of it. Generally, when you find it in a reading, it is the querent’s love life or romantic relationships in general that the Heart refers to.
The Moon is sometimes read as representing a romantic relationship (although I personally never use it for relationships per se.) or the feelings involved. The energy of the Moon card is primarily around how you are perceived, the honour you are held in, feeling, moods and emotion. Think the rise and fall of the oceans, as well as the sometimes unseen, hidden depths. The focus of this card in a romantic or relationship sense would be more in the feelings and moods of romance, the sensations of it, rather than Love at its core like the Heart.
The Ring often denotes a relationship or marriage, but the key element of the Ring’s energy is less on the romantic side of things, and more on commitment. Agreements, vows, promises, contracts, bonds of all kinds are represented by this card. So a married or otherwise “taken” person is likely to be represented by the Ring romantically.
As the Birds are often shown in a pair, a romantic relationship or couple can sometimes be symbolised by this card, literally “Lovebirds”. However, the primary energy behind this card is that of communication rather than emotion or romance