1.004 won't taste very salty, it's only ~15% seawater. Normal marine water is around 1.025 at tropical temperatures.
1.04 is hypersaline water, and if it doesn't taste salt, either you have no saltiness taste buds (that's about 16 times normal sewater salinity!) or your hydrometer is broken or you have mis-read the device.
Hydrometers depend on proper usage for accuracy. They must be cleaned between uses to wash away salt and lime, and they should be floated in a still sample of water (e.g., in a large pickle jar) rather than in the aquarium. Water currents will cause them to bob up and down, making it impossible to read them accurately.
Hydrometers also depend on calibration. Aquarium ones are calibrated to work at 25C, ones designed for other purposes, such as brewing, will be different. It should say what they are calibrated to on the hydrometer or its original packaging.
Also, make sure you ignore the meniscus, the bit of water that "crawls" up the stem of the device.
A plain vanilla hydrometer is the simple glass kind that floats in water and looks like a thermometer. The kind I have and use. Cost £4.98, and been in my care for about 20 years.
Cheers, Neale
I have a cheap floating hydrometer that looks like a thermometer but I don't trust its reading. I always keep spare 30G of brackish water for water changes and its reading is at 1.04 but when I taste it, it doesn't even taste very salty.
Neale mentioned about "A plain vanilla floating hydrometer (around $5) ". What is this exactly?