Not really. That's like saying that all lamps over 300 watts are to be called lamps and those less than 300 watts are to be called light bulbs. A difference between control voltage and switching voltage isn't really a discriminator either.
Is the "condenser" in the ignition of your pre-1980s car not a capacitor, just because the auto mechanic calls it by that name?
There is a difference. Contactors are usually used when driving motors. They have a higher voltage rating to prevent arc-over when stopping a motor. Relays are often used in control circuits and have lower voltage ratings. N.B. There is a voltage rating for the coil that pulls-in the contacts, and a different voltage / current rating for the contacts that drive the load..
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