One difference is microcontrollers are usually designed to perform a small set of specific functions whereas microprocessors are for huge, general functions.
Anything else??
A microcontroller is a microprocessor (a.k.a. CPU core or cores) with additional peripherals on-chip. The terms come from the 1970s, where a microprocessor (e.g. Motorola 6800 or Intel 8086) would have an address bus, a data bus, and control lines, and a microcontroller (e.g. Motorola 6801 or Intel 8051) would have peripheral I/O pins (serial ports, parallel I/O, timer I/O, etc.) but no external memory bus (you were stuck with what was on the chip).
Additionally, microprocessors executed their programs from external ROM and microcontrollers would use internal masked (as in "programmed at the factory by changing the IC photo mask") ROM. The only practical erasable ROMs were UV-erased EPROMS, electrically erasable PROMS (EEPROMS) were expensive, slow, and not very dense, and "flash" meant the bits of plastic sticking out of the mold seam lines on the chip.
Honestly, the line between them is fading away. Modern microcontrollers such as the Motorola 6812 series have an external memory bus and peripheral I/O pins at the same time, and can be used as either a microprocessor or microcontroller.