The way it handles low temperature alarms are very different as well. The basic it is just a squeeker it makes lots of noise so you know to go check it. Unless you are not there. The HS one can be set so that if the probe suddenly goes cold the unit can kill power and squeal.
A good friend of mine bought a one (on my recommendation) for Christmas last month his cat playing with the dangling probe cord pulled the probe off the heat source, He came home to a squeeking herpstat and cool snakes, the basic would have tried to heat the probe (the cat was playing with) by maxing out the heater potentially cooking the snakes. It is quite a big difference. With the relay you likely do not need a failsafe without one? I would say you do need a failsafe, IMO it is not optional.
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