Are watts usually measured in watt-hours?
Energy is an amount, while power is a rate at which energy is used.


Energy is measured in watt-hours (W·h) or joules (J).  
Power is measured in watts (W) or joules per second (J/s).


Watt-hours are like buckets, and watts are like buckets per hour.  If you have 5 buckets of energy and you pour one bucket per hour, you'll be able to pour for 5 hours before you run out.

If you turn on a 60-watt light bulb for 1 hour, you have used 60 watt-hours of energy.  If you use it for 2 hours, you have used 120 watt-hours of energy.  If you turn it on for only 1 minute, you have used 1 watt-hour.

It's a little confusing since the "per hour" is inside the term "watt", so to make the rate into an amount, you need to multiply by a time unit to cancel it out.

It would be a lot more intuitive if we worked in kilojoules and kilojoules per hour.   :)