Whenever you hear reference to "assembled struts", the term is referring to the strut, plus coil spring, plus top hat. You'll find that most reputable off road suppliers offer assembled struts as standard in all of their kits, because this makes DIY installation super-simple.
When you're buying a kit, make sure it offers assembled struts.
A kit with assembled struts will incur a labour charge, but it's money well spent. Just make sure that wherever possible those struts are assembled by the manufacturer. The required inclusion of top hats or strut tops is another expense to allow for.
If needs to be this way in off road vehicles because coil springs fitted have a very high spring rate, which requires the use of expensive mounted spring compressors, which you probably don't have laying around in your garage, no matter much of a budding mechanic you are.
URGENT WARNING - ASSEMBLED STRUTS
Do not even think about using a simple threaded spring compressor, such as the types which clip onto the spring and wound up with a spanner or rattle gun. This is incredibly dangerous. It's not worth the risk. Don't do it!