Electric heat will transform electrical energy directly into heat, this generally has an "efficiency" of 100% because all of the electrical energy you use, gets transformed into heat. It's not really ideal though because electrical energy is a more sort of "refined" form of energy, in that you can use it to do a lot of things, and depending on where you're getting it from, there might be a bunch of fossil fuels burned to generate it.
E.g. if your electric power comes from natural gas fired plants, they might get a typical efficiency of about 40%, so forty percent of the energy in the natural gas is turned into electric energy, and then transmitted to your house, where it is converted to heat. A natural gas furnace, on the other hand, takes the natural gas into your home, and burns it to directly produce the heat. Modern furnaces can capture somewhere about 95% of the heat in your home.
Electric heat is way simpler, and there are other issues with running a system of natural gas pipelines all over, but clearly on a "how much of the original energy winds up causing your home to be warmer" criteria, the gas furnace is better.
Heat pumps, on the other hand use electric power, not to generate heat energy, but rather to pump heat energy from outside your home to the inside of your home. Heat naturally wants to flow from higher temperatures to colder temperatures, but if you're willing to pay for it (by adding more energy) you can "pump" it from cold to hot. (Like water wants to flow from high elevations to low elevations, but you can make it go the other way with a water pump.)
The fantastic thing is that with 1 unit of electric energy, you can usually move way more than 1 unit of heat energy. With relatively new models made in the last few years, if it's not too cold out, you can often get up to 5 units of heat to warm your home for every 1 unit of electric energy. That's like having an (impossible) electric heater that operated at 500% efficiency. And even as long as the performance is about 2.5, which is very reasonable for modern heat pumps, it's even more efficient to use a gas powered electric plant to create electricity and using that to run a heat pump than just burning the gas directly for the heat.
So I suspect, under normal conditions your heating is provided by the heat pump. When it gets really cold, it may just not be able to produce the volume of heat required to maintain a reasonable temperature, then the emergency heat would allow you to turn on direct electric heating (which would be much more expensive than you'd be used to, to output the same amount of heat it would likely use 4-5 times as much electricity...)
So long story short, it sounds like you should continue using your heating like you have been, but what's actually happening is likely the reverse of what you've been led to believe. The normal operation is using the heat pump, where the electric energy is being used to pump heat to the indoors from the outdoors, while the emergency heating is there for conditions where it's too cold for the heat pump to do its job effectively, and turns electric energy directly into heat.
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