Android phone basically have two different dual SIM systems, AFAIK:
DSFA (Dual Sim Full Active): both SIMs can receive calls simultaneously, and you can switch between one call and the other
DSDS (Dual Sim Dual Standby): when one SIM is receiving a call, the other one is in standby. It will receive nor calls, nor SMS. It is like the second SIM is put in a phone turned off. As soon as the call ends, both will return to active state.
For more details, this page from NGM is pretty explicative.
Like DSFA and DSDS, also network coverage for different SIMs is all on the manufacturer's choice: I once had a cheap Dual SIM phone (not even a smartphone) which had a UMTS first slot and GSM second slot, but there are phone who can offer LTE on both.
Android also allows to select a favorite SIM for various action: you can always choose which number you want to call or send from, but if you have a plan good for messages and one made for voice call, you can tell Android to send SMS from the first SIM and calls from the second, unless specified otherwise. So, you don't risk spending more than you should when forgetting to tell which SIM you want to use for a call, or to switch SIM.