often the two terms are the same, but they can mean two different things.
A true voltage stablizer only adjusts the low voltage (sags) and high voltage (surges) back to the nominal line voltage 115 to 120 volts AC. The actual voltage on your utility supplied line can vary +/- 10% or more during a normal day, but the real concern is when the voltage drops and approaches "brown out" conditions. The stabilizer should have the circuitry to modify the input voltage and get it back up to 120VAC, within certain design limits. If the voltage drops too low, the unit should automatically shut off.
A true "power conditioner" should do all the stabalization work plus filter any electro-mechanical interference (EMI) and radio-frequency interference (RFI) that is hitch-hiking on the AC line as well. A good power conditioner will also have the shut down circuitry for excessive low or high voltages as well as typical "spike" surge suppression. Not all power conditioners are the same. Sadly, some manufacturers build their equipment to only deal with high voltage conditions, totally ignoring low (sag) voltage conditions. You have to read the spec's carefully, because this is never mentioned in "large print".
