What is the relation between these two concepts?
Can you tell us what you know so far? The two concepts are fairly different...
I have initial information about both waves and their characteristics but I am confused to find a relation between the two when it comes to make a comparison.
It is not obvious in what context you are asking the question. I think a modulated continuous wave could be radiated as a time varying series of plane waves, kinda.
A plane wave is an EM wave that is propagating after travelling a moderate distance (a few wavelengths) from its source (like an antenna or other EM radiation source):
Your term "modulated continuous waves" would just seem to imply that the EM waveform carries some form of modulation on it, whether it's AM or FM or some other modulation scheme:
Modulated continuous waves could be carried on wired transmission lines, which would not qualify as "plane waves". Or the modulated continuous waves could be FM radio transmissions that you receive in your car as you drive around the city, and those are indeed plane waves carrying the sound information.
Please read those two web pages in detail, to see if they help to answer your question. If you still have specific questions after reading those pages, please post them here in this thread.
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