"1 terabyte is 1000000000000bytes, or 1 trillion (short scale) bytes, or 1000 gigabytes" - http://en.wikipedia.org/wiki/Terabyte
A byte is the next largest unit in cs. It is equal to 8 bits, so it can have 256 different values. The unit abbreviation for byte is 'B'.
There are two scales for measuring large amounts of bits and bytes. one is the base 10 scale from SI that we know and love, the other is base 2. The prefixes that we use are, in order from smallest to largest: 'kilo' 'mega' 'giga' 'tera' 'peta'..., and the abbreviations are 'K' 'M' 'G' 'T' 'P' ...
When using the SI scale, there is an order of magnitude difference of 1000 or 10^3. Eg, 1 Mega_ is 1000 Kilo_. When using the base 2 scale, the order of magnitude difference is 2^10, or 1024. Eg 1 Mega_ is 1024 Kilo_.
When it is not clear from context what scale is being used, you can specify base-two by replacing the second syllable of the prefix with 'bi', so the scale becomes 'Kibi' 'Mebi' 'Gibi' 'Tebi' 'Pebi' ..., and the abbreviation become 'Ki' 'Mi' 'Gi' 'Ti' 'Pi' ... These abbreiations aren't widely used, however, and there is no way to specify that you mean to use the base 10 scale.
This isn't a huge issue, though, because aside from large scale storage (anything bigger than RAM) and sometimes networking, base 2 is assumed.
Eight bits in a byte is a "de facto" standard so it is a "typically" safe assumption on most modern hardware, but the actual definition of how many bits are in a byte is hardware (and situation) dependent. There is no definitive or formal standard that defines how many bits are in a byte. The range is often between 7 to 12 bits per byte, but I think some really ancient systems (1940's - 1950's) were below 7 bits per byte.