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What is the difference between character '1' and integer 1 in terms of C plus plus?
Characters and integers are two different types: 'char' is an 8-bit unsigned integer (normally), while 'int' is a 16, 32 or 64-bit signed integer.
Ints and chars are both integer numbers internally, but their numeric values are interpreted differently: The numeric value of the integer 1 is 1 (reasonably enough :), while the numeric value of the character '1' is 49.
Characters are represented in computers by using a table mapping from integers to characters. The most common mapping is ASCII, and in the ASCII table the character 1 happens to have the numeric value 49. (I assume they didn't put it on 1 because all the values below 32 were reserved for system commands like 'bell' and 'escape'.)
See related link for the ASCII table.
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