These two cast ons, the knitted cast-on and the cable cast-on, are very similar. But there are a couple of differences I wanted to talk to you about as well as what they can do and when they should (and shouldn't) be used.
One of the nice things about these cast-ons is that they don't require you to decide how much yarn to leave for the tail as does the long-tail cast on. No worry needed about running out of yarn during this cast on. You just start with a slip knot, leaving as much tail as you need for weaving in (6-8 inches). So that's a big positive for both of these cast-ons.
So you might be wondering something like: If I don't have to worry about leaving a long tail and possibly running out like the long-tail cast-on, why would I ever do long tail cast-on again? Shouldn't I just switch to one of these cast-ons and leave that long tail behind?
Nope. Sorry. Although these two cast-ons have that big benefit, they also have a drawback: lack of elasticity. The knitted cast-on is fairly firm; it has a slight stretch to it, but not that much. And the cable cast-on is very firm with little to no stretch. So when you have a project where you need the edge to be more elastic (the brim of a hat or a lace shawl that you want to be able to block and stretch, for example), this shouldn't be your go-to cast-on.
So when should you use either of these cast-ons? Well, when you want an edge where you don't need that elasticity. For example, the cable cast-on is perfect if you are doing a buttonhole that needs you to cast on stitches. That lack of stretch will help hold that buttonhole in place so the button won't pop out. (And here, since the cable cast-on is more firm that the knitted cast-on, use the cable cast-on for the buttonhole scenario.)
This is also a good cast on when you need to add a few stitches in the middle of some knitting because of how these cast-ons are created. It will allow you to add the cast on stitches without any gap between the previous stitches and these new stitches. Have you ever tried to do long-tail cast on in this situation? It's pretty much impossible. And the backwards loop cast on works, but it's not as steady.
One benefit to the knitted cast on is that it's really easy for a beginner knitter to learn because what you're ultimately doing is just knitting a stitch and then placing that stitch on the left-hand needle. So the beginner knitter who has gotten the knit stitch down would find this an easier cast on than the maneuvering needed for long-tail cast on. (Just remember the trade off of a less elastic edge.)
Another negative of the knitted-on cast on is that although it is a fairly firm edge, it's easy to stretch it out of shape. The extra firmness in the cable cast on won't stretch out of shape as much. So again, think about the needs of your project to determine which cast on is best for you.
One other thing to keep in mind (which I mention in the video): you can place the stitch you've created on the left-hand needle in either direction. There are some differences based upon which direction you choose, but the main thing is to make sure you are consistent. Pick one way to mount the stitches and stick with it through your cast on. Otherwise, you'll end up with a wobbly cast on.
As for which direction you choose, that is up to you as one way will mount the stitch so the right leg is forward and the other so the left leg is forward. How you work the next row will determine if you are twisting that cast-on stitch. If you want to add even more firmness to the knitted cast-on, then check the mount of the stitch. If the right leg is forward, knit through the back loop to twist the stitch. If the left leg is forward, knit through the front loop to twist the stitch. Twisting the stitch will tighten things up and add even more firmness.
Here are the two cast-ons so you can compare. The cast-on edge for each sample is the bottom edge. The sample at the top is the knitted cast-on, and the same on the bottom is the cable cast-on. (Don't compare width of the samples as I did not cast on the same number of stitches.) You can see that they look very similar but the top one (knitted) is not quite as tall as the bottom one (cable); it's just slightly more spread out vs the cable being slightly more bunched up. (Fairly firm vs. very firm)