A bass guitar is basically an electric guitar without the first two strings and tuned down an octave. The strings are further apart and the neck is longer to facilitate the lower tuning. There is however the more modern 5 and even 6 string bass guitars being used today. They have an extra B string added to go even lower than the traditional 4 string bass. I would recommend a beginner go with a 4 string bass.
Basses come with bolt on necks as well as glued in or "set" necks. Bolt on necks are more durable. Like the guitar, a bass has different scale lengths. Scale length is determined by the distance between the nut and bridge of an instrument. In most cases a small scale bass would be best suited for a child. There are various types of pickup scenarios available with things such as built in preamps. These are to add gain and to adjust the sound before it gets to the amplifier.
The bass will need an amplifier. Try and get an amplifier with at least a ten inch speaker in it. As with the electric or acoustic guitar, there are many different all-in-one packages out there which include everything you need to get started.
Make sure where ever you buy your guitar it comes with a return policy. If you don't have experience with the guitar, you should have someone who is an experienced player inspect and play the instrument before you commit to buy it.