1. They do not convey the same amount of information. Take 发 for example. This is now a split tone word which can mean either 發 or 髮. The information density has been reduced and it's now ambiguous without context which character this represents.
2. People in Mainland China and Taiwan most certainly do not speak the same. There are a litany of spoken differences between 普通話 and 國語. As someone who travels frequently between the two countries, I am constantly shocked how much the two have deviated. There are numerous idioms that are completely unused on either side. Many very basic terms such as the terms for SMS (短信 in China, 簡訊 in Taiwan) are completely unrecognized outside of the respective areas.
2. People in Mainland China and Taiwan most certainly do not speak the same. There are a litany of spoken differences between 普通話 and 國語. As someone who travels frequently between the two countries, I am constantly shocked how much the two have deviated. There are numerous idioms that are completely unused on either side. Many very basic terms such as the terms for SMS (短信 in China, 簡訊 in Taiwan) are completely unrecognized outside of the respective areas.