How are two definitions of baud rate same?
The letter 'A' is not a symbol in this context. A symbol is a recognizable distinct value on the communication channel; it is a quantum of transmittable information.
For a binary communication channel, a symbol is either a 0 or a 1. If you are talking about conventional UART kinds of transmission, then every transmitted byte of information will also need a start symbol and a stop symbol. So, you have to transmit 10 symbols in order to transmit 8 bits of information. The maximum information (bit) rate is 8/10 of the maximum baud rate.
Some kinds of communication can send multiple bits per symbol. In the old fashioned touch-tone dual-tone multiple-frequency (DTMF) telephone systems, pressing a button on the keypad caused a sound to be transmitted. Each sound was a symbol. Each sound comprised two audio frequencies, one frequency corresponding to a row on the keypad and the other frequency corresponding to the column. With four rows and four columns, each sound corresponded to 1 of 16 keys. So, each sound conveyed 4 bits of information.