An important thing with ICD instead of ICE is that it can be used for standard factory testing.

Since it doesn't require extra hardware (besides a JTAG/BDM/xxx) connector or just pads for a bed of nails, the production process can use it to program flash (including boot loader) or to (at least for some architectures) download test programs directly into RAM to wiggle all I/O signals, and verify UART in/out, SPI, I2C, ... giving a very high test coverage without expensive hardware. In many situations, the ICD is enough to very clearly point out production issues even when the target hardware is unable to run. In the microcontroller world, it's now common to have internal RC oscillators in the processor allowing the factory testing to be performed with just a stable supply voltage (which is obviously easy to verify externally) and working signals for the ICD interface.

An emulator (ICE) on the other hand is used with a specially prepared target hardware so expensive (together with the emulator and target-specific probe) that newer emulators normally have ethernet interfaces just so a large development team can share the single setup, basically booking time with the emulator similar to how software developers once had to book mainframe time.