On the ZX80, ZX81 and ZX Spectrum, tape output is achieved by the CPU toggling the output line level between a high state and a low state. Input is achieved by having the CPU watch an input line level. The very low level of operation was one of Sir Clive's cost-saving measures; rival machines like the BBC Micro had dedicated hardware for serialisation and deserialisation of data, so the CPU would just say "output 0xfe" and then the hardware would make the relevant noises and raise an interrupt when it was ready for the next byte. The BBC Micro specifically implements the Kansas City Standard, whereas the Sinclair machines in every instance use whatever adhoc format best fitted the constraints of the machine.
The effect of that is that while almost every other machine that uses tape has tape output that sounds much the same from one program to the next by necessity, programs on a Sinclair machine could choose to use whatever encoding they wanted, which is the principle around which a thousand speed loaders were written. It's therefore not impossible that different programs would output distinctively different sounds. Some even used the symmetry between the tape input and output to do crude digital sampling, editing and playback, though they were never more than novelties for obvious reasons.
That being said, the base units of the ZX80 and ZX81 contained just 1kb RAM so it's quite likely that programmers would just use the ROM routines for reading and writing data, due to space constraints if nothing else. Then the sound differences would just be on account of characteristic data, as suggested by slugster.
