What is the difference between ESP8266 and Wemos D1 Wi-Fi Module.
Is there any difference in programming part for both of them.
Which is more suitable with Arduino Uno.
WeMos D1 is an ESP8266 module with power and USB support circuitry and Uno style headers. It's a substitute for an Uno, not something you'd use with an Uno. Think of it as an Uno with WiFi communication that runs at 3.3V instead of 5V and is significantly less beginner friendly.
If you want to use an ESP8266 with an Uno you should either get an ESP8266 module and the necessary components to supply > 500mA@3.3V(the 3.3V pin on a standard Uno will not be sufficient) or get an ESP8266 shield that plugs into the Uno.
NVT123:
Is there any difference in programming part for both of them.
For programming them directly, no, an ESP8266 is an ESP8266. However, if you're wanting to use an ESP8266 with an Uno then you're probably going to send the commands from the Uno to an ESP8266 running the AT firmware over serial using AT commands. This will require different code than if you were uploading your code directly to the ESP8266.
The D1 mini is breadboard friendly, that is the pin spacing will plug into a standard breadboard. It has fewer I/O pins than a standard Arduino. But it has more memory, and runs faster. Now that the library has been updated, you can program it right from the Arduino IDE, with no AT commands needed.
I think it is a great little board, and inexpensive, because everything you need to get going is built into it.
I agree about the D1 Mini being nice. I think it's way better than the Uno style D1. The regular D1 is pretty much the same thing only 4x bigger and with the idiotic Uno off grid header. The only real reason to use the regular D1 is for shield compatibility but there might be issues with the 3.3V I/O, I'm not sure there's some confusing information on whether the ESP8266 is 5V tolerant or not. I own both but the only reason I bought the regular D1 is because it was falsely advertised as being a shield.
That said, the D1 Mini is not really intended for use running the AT firmware to communicate with a regular Arduino. You could do it but there's not much point in all the USB stuff on there if you're not programming it directly.