When selecting cables for DC current, there are 2 mains concerns from an electrical point of view :
- the voltage drop, which is directly related to the resistance (and the current), which in turn depends on the section (gauge) of the wire, its lengths and the material of the conductor. This is particularly important for long wires in a low voltage - high current setup
- the ampacity of the wire (ie will the wire overheat/burn/cause fire). This depends on the resistance per distance of the wire (ie section + material), the ambiant temperature, the environment (ex : ventilation, insulation around the wire, cable bundle or not, ...). And last but not least, the insulation of the cable itself : some start melting at very low temperatures, other at far higher temperatures. Once the insulation has melted, you often get a short circuit (generating even more heat).
So to answer your question about why such a difference, I think the main reason is that the toolbox calculator computes the ampacity based on standart insulation (ie rather low melting point), whereas on the picture of the amazon wire, it is written 200°C, which is a high temperature rating.
A wire with 200°C temperature rating can carry far more heat before reaching the melting temperature of insulation than a standard wire. Still, I don't think it's a good idea to get your cable really hot (it might still destroy sensitive components nearby (for example your Lipo, which will then explode), or make some materials ignite, or you might burn your fingers).
And always take the marketing data from amazon vendors with a pinch of salt : they often overstate the quality of the product, especially on hard to test aspects.
If you wish to use that cable, I would suggest you do a simple test : you first force 1A through the cable for a few minutes, then touch it. If it is cool, then you proceed with 2A, 3A, ... until 8A.
If at 8A you can still comfortably hold it in your hand, you should be fine. If at any point it hot, then I strongly advice against using it (at best you will waist lots of energy, and worst it might melt).