ATTINY45 is high performance, low power controller from ATMEL. It is an 8 bit controller based on Advanced RISC architecture. It is one of members of ATTINYXX series, popular because of its small size and features.
ATMEGA328P is high performance, low power controller from Microchip. ATMEGA328P is an 8-bit microcontroller based on AVR RISC architecture. It is the most popular of all AVR controllers as it is used in ARDUINO boards.