Mandarin and Chinese could be same and different. So yes, they are the same on the society aspect (historically and politically). And no, they are not the same on the natural aspect (linguistically and ethically).
Mandarin is one of the languages (a dialect) spoken by northern people in China, and Chinese is a umbrella term inclusive of all the languages (all dialects) spoken by all people in China. Since the PRC and ROC were founded in 1912 and 1949 respectively, the Mandarin is now seen as a representative of Chinese languages. Nowadays, Mandarin is taught throughout mainland China and Taiwan in schools, and few Chinese people speak their dialects. Besides Mandarin, Cantonese, Hakka, Hokkien, Teochew, Wu, Gan, Fuzhou are also Chinese dialects.
Mandarin could be written in both simplified and traditional Chinese characters. Traditional Chinese is used in Hong Kong, Macau and Taiwan, and simplified Chinese is used in mainland China and Singapore. Simplified, funnily enough, appears much more simple to read and write, whereas Traditional comes across much more complex at first glance. Learning Mandarin in a natural approach, you do not have to decide to learn simplified or traditional Chinese characters in the beginning. Since it is shared by the most Chinese around the world, you can make the decision after you are familiar with basic Mandarin. At that time, you will have better knowledge and confidence to chose from two kind of Chinese characters.
Do not worry about the delay of learning Chinese characters. Chinese kids start to learn Chinese characters at the age of seven. Before seven years old, they experience the language around them and no one is forced to repeat what they heard. They interact with adults in their way, and no one blame them. It is a wise choice to start with listening.