Here is an awfully incomplete answer :
By doping, oxyding, metallising a slice of sillicon, you can create on the surface several types of components : wires, bipolar transistors (aka BJT), metal-oxyde transistors (aka MOS), resistors, inductors, capacitors... (but it is often easier to create a transistor than these passive components).
Components are created at once by applying patterns and exposing the die. Transistors are not 'pick and placed', even for analog integrated circuits.
Bipolar transistors used in TTL gates are 'current controlled' and work very differently than MOS transistors which are 'voltage controlled'.
TTL (transistor to transistor logic) is traditionally defined as logic levels and I/O characteristics, which were (in the '70s-'80s) optimal for bipolar transistors working with 5V power supply. It is now possible to build with MOS transistors chips compatible with the TTL logic levels.
Logic gates can be created with bipolar and MOS transistors, but, nowadays, MOS is used almost exclusively for creating logic circuits like microprocessors, memories...
Bipolar transistors (and j-fets) are currently mainly used in analog components (for example operational amplifiers).
It is possible to mix bipolar and MOS on a single die, but the additional number of steps and constraints makes that technology more expensive and reserved to specialty component (for history, the first Pentium used BiCMOS which mixes bipolar and CMOS, this technology is nowadays used for analog or mixed signal components like ADC/DAC)