There are different reasons for all types of wire and cable including bare copper. Sometimes wire has insulation and sometimes it does not for specific reasons. Engineers work hard to provide a type of wire for every application out there with approvals to go with it.
Bare copper is also known as a ground wire. It is not insulated at all so it has no protection. It is mostly used in homes as a ground wire and has the best conductivity without insulation. So as long as it is not going outdoors then electrical contractors do not mind using it.
Bare copper is also the base for most types of wire and cable. It comes solid or in smaller awg sizes wrapped together to equal the same gauge. Using the smaller awg sizes gives the wire more flexibility to bend around corners. You might think that you would always need the most flexible because it could only be better but that's not always the case. Sometimes electrical contractors need it to be more stiff so they can send it a long way through conduit.
A green THHN wire is also known as a ground wire when the wire needs to be outdoors. Green calls out the fact the THHN is a ground wire and the reason for the insulation is so it has protection against moisture. It can then go outdoors and in conduit while it still acts as a ground wire. The reason for using it indoors without insulation is simply because it's cheaper. Sometimes you might see this wire with a yellow stripe as well.
There is not always a ground wire in every cable. If you need one then I recommend talking to your cable sales person and making sure they know that as well. Most companies that supply wire also supply the bare copper so you should not have a problem getting it if you need it. You can usually request a specification sheet to make sure you are getting the exact cable you are looking for.