I had been having some discussions regarding Multi-SIM phones and there is a bit of misunderstanding so here is my clarification about them. Anyway, a lot of information is just an understanding so feel free to correct any mistakes you think I may have made.
This post is about multiple SIM cards, physical UICC cards rather than single UICC with multiple SIM applications. We will look at Dual IMSI later on in the post. In case you do not know about the multiple SIM applications in a UICC, see this old post here. In this post, I will refer to UICC cards as SIM cards to avoid confusion.
Back in the old days, the Dual-SIM phones allowed only one SIM on standby at any time. The other SIM was switched off. If someone would call the number that was switched off, a message saying that the number is switched off would come or it would go in the voicemail. To make this SIM in standby, you would have to select it from the Menu. The first SIM is now switched off. The way around it was to have one SIM card calls forwarded the other when switched off. This wasn't convenient and efficient, money wise. The reason people use multiple SIM phones is to have cheaper calls using different SIMs. So in this case forwarding calls from one SIM to another wont be cost effective. These type of phones were known as Dual SIM Single Standby or DSSS. These devices had a single transceiver.
So as the technology got cheaper and more power efficient, the new multi-SIM devices could incorporate two receivers but only one transmitter was used. The main reason being that using two transmitters would consume much more power. As a result, these devices can now have both the SIM's on standby at the same time. These kind of devices were known as Dual SIM Dual Standby or DSDS. Wikipedia also calls then Dual SIM Standby or DSS. This concept could be extended further to Triple SIM Triple Standby or TSTS in case of the device with three SIM cards and Quad SIM Quad Standby or QSQS in case of four SIM cards. One thing to remember is that when a call is received and a SIM becomes active, the other SIM cards become inactive for the duration of the call. A workaround for that situation is to forward the call to the other SIM card in case if its unavailable. Though this will work for DSDS, it may not be that straightforward in case of TSTS and QSQS due to more than two SIM cards being present.
Another category of devices that are now available are the Dual SIM Dual Active or DSDA. In this case there are two transceivers in the device. Both the SIM cards are active at the same time so each SIM card can handle the call independently of each other. It would even be possible to conference both these calls.