Hi, yes it's true that every style has its own metrics. In classical music, every musical "Form" has its own metrics. In other types of music, even light music or Jazz, other types of Metrics are observed.
In light/pop music, which from what I have understood from other posts interests you directly, the metrics are essentially structured into verses, choruses, bridges, and codas.
Different combinations of these 4 essential elements can be created. The combination of these elements creates a form.
The verse is that which, broadly speaking, can be traced back to the "theme" of classical music. Therefore, first verse and second verse are equivalent to the first and second themes in classical music. However, while in classical music the second theme was different from the first theme, in light music they can be musically identical, but the meaning of the lyrics can change. The idea changes in the second verse or the concept expressed in the first verse is expanded. We then have the chorus that everyone knows, which is that part of the melody (and this time of the lyrics) that is repeated and can be exposed repeatedly within the composition. We almost always have a bridge. The bridge is what is called a modulating bridge in music, but beware, in light music it is not always modulating! In light music, in fact, it is also normal to modulate at the end of a verse or a chorus. The modulating bridge is that melodic ornament that connects the first part of the composition written in one key to the second part written in another key. In light music tracks, modulation to nearby keys is very frequent (See the circle of fifths); I have never seemed to observe modulations to distant keys, including changes of mode (which are instead often used in classical music). The reason is that art music allows for a much broader and more sophisticated harmony that admits strange modulations such as the enharmonic modulation of the diminished seventh, with which it is possible to modulate to any key from any key we find ourselves in. (But it is very peculiar and strange to the ear, which is why it is not used in light music). I have only happened a few times to hear even in light music modulations by imitation, or as my teacher used to call it, modulation with the "fan" technique, because one modulates by imitating the bass with other voices (tenor, alto, or soprano) moving through the entire circle of fifths until reaching the key we are interested in (a method that is found very much in Bach).
Finally, there is the coda, which is that portion that, as the term suggests, concludes the musical piece.
It's true, by giving importance to metrics, memorization is easier, precisely because you know at every moment where you are within the piece. And yet, a harmonic analysis of the piece is important (especially in classical music for the purposes of memorization).