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As you can see from the words, the LC oscillator uses a resonant circuit made of inductors and capacitors. The other uses only resistors and capacitors, not in resonance but to adjust the 180-degree phase shift needed to establish oscillations.
RC oscillators are mostly used at low frequencies, < 1 MHz while LC oscillators are preferred >1 MHz.
Another type of oscillator without coils is an astable multivibrator, a system of two active elements (gates), alternatively closing and opening each of the two through an RC circuit which determines the frequency of oscillations.
While the first two oscillator types generate sinusoidal oscillations, the multivibrators generate rectangular pulses.
I think, such a general question can't be answered. Each harmonic oscillator needs a frequency dependent network with 0 or 180 deg phase shift at one frequency only - and such a network can be realized by an LC or an RC network. However, the disadvantage of inductors (coils) is known: Heavy, expensive, electro-magnetic radiation, ...
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