What is difference btween a Adapter providing DC current 5 Volt 1 Ampere and 5 Volt 2 Ampere.

For practical purposes, you can use either of them. Of course, there are some points to be noted in this context. For getting right power supply, you should match voltage, amperage and polarity.

Voltage
Try to get the voltage as close as possible. Getting the right voltage is the best thing as in your case you have got that. Both your adapters are 5 V. Using a voltage closer, but not exact may shorten the lifespan.

Amperage
The difference in Voltage and Ampere lies in Voltage is what power supply provides, and Amperage is what the device is being powered. In other words, the device may draw more power when it is working hard than when it is not doing so. The rated amperage of a power adapter is the maximum it can provide. So as long as it provides the minimum required amperes or more, the device will have no problems in functioning properly. As in your case, you need a adapter that has 5 V and at least 1A. Thus using 5 V 500mA adapter may harm your device while using an adapter with 5 V 2A is safer.