Your spare power adapter is not as powerful as the original one. Usually, it works anyway but it might be not enough if you run your laptop on full power consumption. In the latter case, your laptop will draw battery power since the power adapter won't be able to supply enough current. You can just give it a (supervised) try and see if it works for your use-case.
But beware, it's at your own risk! Usually, the voltage will just "break down" if the laptop tries to draw to much power so the laptop switches to battery power. But there might be other hazardous consequences as well (see the link Kamil provided for more information). Better to make sure the laptop does not require more power then the power adapter can supply e.g. by limiting the CPU clock rate.
Also, to be save: If the spare power supply is "unregulated" the voltage will change depending on the load. Make sure your laptop can handle voltage "adjustments". E.g. by checking if the original power supply is also unregulated.
In my own experience, if the spare power supplies it from the same type of appliance or a "universal" spare power supply I bought in the shop, I haven't experienced any problems.... luckily. But note: Unless I absolutely have to I don't used "cheap" power supplies from no-name manufacturers.