Text painting, word color, and word painting all mean basically the same thing: the use of music to depict, through direct imitation or a similar technique, the words or subject of a vocal piece. It's basically a subset, one element, of the general way music is made to be expressive of words, emotion, or ideas in the outside world. It can take the form of an imitation of sounds in the real world, a kind of musical onomatopoeia.
Examples of this occur frequently in the classical repertoire. For instance, in Beethoven's Pastoral Symphony, the sounds of bird calls are imitated by the woodwind instruments in both the first and second movements. In the second movement, which is subtitled, "By the brook," the flowing accompaniment in the strings, and perhaps even the principal theme itself, are like the sound of water gently streaming by. In Schubert's songs, word-painting occurs frequently. A well-known example is a song which entered the American popular repertoire in the twentieth century, Serenade (Ständchen). The lyrics depict a man outside a woman's window singing a love song, and the repeated notes in the piano accompaniment sound like the plucking of the serenader's guitar.
In classical music the structure of music—melody, harmony, dynamics of softness and loudness, and orchestration are employed to characterize general ideas and emotions, even more frequently than they're used for simple "word painting." For instance, in Mozart's opera Don Giovanni (Don Juan), in the climactic scene where the Ghost confronts Don Juan and condemns him to hell, the music becomes extremely chromatic and dissonant. This is almost carried to the point of atonality, a technique that did not become commonplace until twentieth-century modernism. Mozart gives the trombones a prominent part in this sequence, because the trombone was always associated with the expression of spiritual and other-worldly matters. It is not literal text- or word-painting, but rather the musical painting of ideas.
In contemporary popular music word-painting and the expression of ideas take varied forms. A few very diverse songs will illustrate this. In Taylor Swift's "You Need To Calm Down" she deliberately delivers the words in a rapid, run-on manner that conveys agitation, the sense that the speaker herself is the one most in need of the advice being given. In many other pop songs, a hypnotic effect is achieved through repetition, especially in the backing or accompaniment, in which there is a typically driving and relentless beat. Coldplay's "Clocks" is an example. The lines:
Confusion that never stops
The closing walls and the ticking clocks....
are symbolized by the repeated arpeggiated figure in the piano. Often in other songs the music seems almost ironic in the sense of conveying the opposite of what the words might imply. In Radiohead's "Fake Plastic Trees," the song has a subdued, almost deadened quality which is simultaneously a contradiction of the anguish the lyrics express and is illustrative of the idea of artificiality, the "fakeness" portrayed in the lyrics.
All of these examples show a range of different methods by which the texts of vocal music are enhanced, or expressed, by the music itself. They range from simple imitation, to the conveying of emotions or ideas, to a subtle irony. In any event, most observers would agree that music, in addition to being expressive of words, changes the meaning of them as they would be if the words stood alone as simply a poem.