Yes, a basic linked turn will very much be a skidded turn. These basic linked turns are typically done with the board at low edge angles at a relatively slow speed. Not all skidded turns are basic however. As you advance your riding, you will begin to use more of a dynamic skidded turn by using more aggressive edge angles and body movements but this a little down the line for you.
You technique is spot on but don`t think of this foot movement as just the toes. It is more of a whole foot movement that originates with the ankle joint; either opening or closing it. The idea is to use this foot movement to twist the board in order to engage the side cut. Related to this torsional twisting concept is edge pressure. This is what the back foot really does as you use it it in a basic linked skidded turn. The front foot starts the process and then the back foot plays a supporting role by pressuring the same edge through turn completion.
As for carving, I suggest that you hold of on a bit before trying to carve. You really need to be comfortable and confident with speed before carving because you need speed to carve and you need to be confident with your edge control before attempting carving. You should be totally comfortable riding steep blue runs making short radius skidded turns within a corridor no wider than one grooming cat at speed. I would say able to maintain 20-25 MPH while doing it before starting to actually carve.
When you start carving, you do not use the front foot first, twist the board method. This is a simple act of tilting the board onto its edge with both feet simultaneously. Your first carved turns will be very basic cross over turns where you incline your entire body over each edge to tilt the board. We call these cross over turns because your entire body crosses over the top of the board much like an upside down pendulum.
You need to have experience and confidence with edge awareness and the ability to fell through your feet whether the board is tracking true or if it is skidding before you carve because in carving, you will transition onto your downhill edge at speed before while the board is perpendicular to the fall line. If the board has any skid when you attempt this, you will catch that edge and eat shit. Work on your skidded turns and edge control a bit before even worrying about carving.
A dynamic turn simply means that you are moving your body a lot and often independently from other body parts. To start making your skidded turns dynamic, at first focus just on lower body movements. Lots and lots of leg flexion and extension. The best drill to get in the habit of this is to flex really low at turn initiation and extend through turn completion, drop low again to initiate the next turns and repeat the process. This is a great first step towards making every turn a dynamic turn...