First, let’s take a look at what rhythm lines can look like.

Elements in the image are aligned, and such alignments don’t happen by accident.


The artist did little studies, and then he found or chose those lines to align things and kept these lines in mind while designing his composition.



After these lines were placed, he aligned things along them. It gives the image a sense of unity.
Nowadays, with cameras, compositions are often designed as shots. The world is cropped in a certain way, maybe all the way up to a close-up.
This is so with movies, which go fast, and you can only look at one spot. So these film shots have to be cropped so you know where to look.
But this is not how the old masters designed their paintings!
They‘d set up an entire scene with people visible from head to toe. What helped was that these were paintings, and you could stand in front of them for a while and study all the rich detail. Which meant it was okay if a lot happened in the painting. The viewer stood in front of it, he wasn‘t going anywhere and had all the time to study the painting.
In designing painted scenes with many people, the masters started with a few quick, rough sketches, and they found these lines that formed in these sketches, rhythm lines people or their limbs were aligned against. And so when they started their paintings, they put these rhythm lines onto the canvas first to align people against. They hired models to pose for them in the required poses, and they set to painting, installing these poses into the painting from live reference or from a drawing made from live reference.
You may find you disagree with the breakdown into rhythm lines I chose - you may see other ones - but you have to admit that you see the nice swervy lines things are aligned against in these paintings. Those don‘t happen by accident, the artist has to consciously design these into the piece.
Construction lines are rigid: they establish a horizontal or vertical relationship between two things, or a certain other angle. They are needed to copy something accurately.
In contrast, rhythm lines are more dynamic and flexible. They are mostly artistic choices: you get to choose which ones you want to use and where to plac e them. They are a tool for composition design. You can move them around, and as long as elements align to them, the illustration can keep looking good as long as the rhythm line relations are adhered to.
Another difference between construction and rhythm lines is that usually, construction lines are drawn up-front, and the drawing made using these pre-determined construction lines while rhythm lines tend to be discovered afterwards. Rhythm lines can form during sketching, while trying out different designs.
An interesting example of this from Proko’s caricature course is to use the Reilly rhythm lines of the head to create caricatures by deforming those rhythm lines.
There are combinations. For example, when drawing in perspective, the placement of the vanishing points is an artistic choice, they are rhythm points, if you will. But the perspective grid lines they generate are a grid of construction lines.
You may choose different rhythm lines, and you may move them around a bit. Aligning things against them will give the whole a sense of unity.
Harold Speed discusses this at length in chapter XII, Rhythm: Unity Of Line of his book The Practice And Science Of Drawing .
Visual designers do use alignment in visual design a lot. You can often tell whether a website or poster was designed by a proper designer or not, just by looking at whether various unrelated visual elements are aligned with each other along invisible lines. This gives the website or poster a sense of unity, simplicity. It makes it look like conscious design choices were made, and not just accidental choices were made.
Alignment helps unify an image and suggests it was designed with intent.