Sleep mode simply pauses the computer. Power is kept supplied to the memory (RAM) in the computer so that everything is still in place but nothing is changing.
Powering off, forces all of the applications to close before shutting down the computer completely. Everything in progress is ended. All reasonable applications on the computer will try to save all in-progress work first. Often you will be asked if you want to save things. If you don't the work is lost.
Sleep is generally much faster and is reasonably safe - AS LONG AS - you dont leave a laptop in sleep and not attached to the mains for more than a couple of days. Sleep mode still uses power, if the power is lost, so is your data. Powering off is always safer but much slower.
To avoid issues when sleeping a laptop, simply make sure everything is saved before you sleep the computer.
There is a third option, "Hibernate". You might need to turn this on in the power settings for the laptop. In this mode, the computer saves the current state of the active memory onto the hard disk and then powers off. When you restart, it reloads the memory from disk. This has the advantage that it requires no power from the battery or mains. However, it is somewhat slower to into and out of.
So quickest is Sleep but it needs a bit of power to keep going. Great for getting out of the office quickly when you know you'll be plugging back into the mains within a couple of days or so. Next is Hibernate, a bit slower but no power needed, OK for going away on holiday for a couple of weeks. Last is power off, the safest but slowest.
Also note, if you have classified information (secret or above) on your laptop - DO NOT SLEEP - you must either hibernate or power off. Otherwise, security information might be readable from memory.
One final point on "is it safe". It is normally safe. But, some computers do fail to resume reliably. This is mainly due to faulty graphics drivers. Always save before sleeping. Indeed, that is a standard to live by!