Short answer: "jade" is one name for two minerals. Nephrite is the more common one, and the jade of most carvings and rings; jadeite is rarer and is the material behind the very expensive bright green pieces from Myanmar. Both are remarkably tough, both feel cool and dense in the hand, and both are easily confused with other green stones that borrow the name.
Two minerals, one name
Nephrite is a calcium magnesium silicate built from felted, interlocking fibres. That structure is why it is so hard to break: it is not the hardest stone (6 to 6.5 on the Mohs scale) but it is one of the toughest, which is why it was used for axe heads before it was used for jewellery. Jadeite is a sodium aluminium silicate, slightly harder (6.5 to 7) and more granular, and it can reach a more intense, translucent green. The two were only told apart chemically in the nineteenth century; before that, every culture that carved them simply called both jade.
Properties you can notice
Jade feels cold when you first pick it up and warms slowly, because it conducts heat well. It is heavy for its size. Under a lens, nephrite shows a fibrous, slightly oily-looking surface, and jadeite a finer granular one; neither contains gas bubbles, which glass does. Colours run from white through every green to lavender, yellow and near-black, and the colour is usually uneven rather than flat.
How to tell real jade
At home you can rule things out, but you cannot confirm. Bubbles mean glass. A warm, light feel suggests plastic or resin. A steel point scratching the surface easily rules out both jades. A flat, perfectly even bright green is suspicious. Beyond that, the honest answer is that nephrite, jadeite, serpentine, dyed quartz and glass can look alike to the eye, and only a gem laboratory with the right instruments can tell you which one you have and whether it has been dyed or impregnated with polymer. Trade names make it harder: "new jade" is usually serpentine, "Malaysian jade" is dyed quartz, and "jade glass" is glass.
What a seller can do is tell you plainly what the stone is and how it has been treated. On our product pages the stone in each piece is named as we know it, and where a stone is dyed or created, that is stated.
Caring for jade
Jade asks for very little. Clean it with warm water, mild soap and a soft cloth. Avoid ultrasonic cleaners and steam if the piece might be dyed or polymer-treated, and keep it away from strong chemicals and sudden heat. Its toughness means it survives knocks that would chip many stones, but a hard edge can still mark a polished surface, so store it on its own.
In short
Jade is nephrite or jadeite: tough, cool, dense and usually green. Many "jades" are not. Rule out glass and plastic at home; leave the final word to a laboratory, and buy from someone who tells you what the stone is.