There is only one library for I2C, that is the Arduino Wire library: Arduino - Wire.
For less than 1% of the situations there are other compatible libraries, for example a software I2C library.
You should ignore the util/twi.h. That is just a low-level part of the Arduino Wire library. Don't think about it it is there, that's all.
If you want to write code for an Arduino, then you should use the official Arduino Wire library. When you later change to another Arduino board, then the I2C will still work with the same functions.
The Dallas 1-Wire is something completely different.
The most used Arduino library for the Dallas 1-Wire is called: OneWire.
There are other libraries that have "Wire" in the name.
For example: "VirtualWire". It has nothing to do with I2C and also nothing to do with 1-Wire.