What is the difference between a dual SIM phone and a two (double) SIM phone?

In two (double) SIM phone, only one SIM card can be standby/active at a time.

In dual SIM phone, both SIM cards are available at the same time when the device is not being used (so-called 'dual standby'), but while one SIM card is active, for example, making a call, sending or receiving a message, or transferring data, the other is unavailable.