Those are different things.
I am assuming you are talking about digital communications.
- Modulate: to change the characteristics of a carrier wave (usually high frequency sinewave) to send data. Some common types of simple digital modulation: OOK/ASK, FSK, PSK, etc... A modulator takes the carrier, the baseband signal, and outputs the modulated signal;
- Demodulate: the reverse. A demodulator receives the input modulated wave and outputs the baseband signal.
The baseband signal may be encoded, such as Manchester encoded, biphase encoded, and so on.
Relaying is just receiving a signal and forward it to other place. Depending on the technologies involved, your signal may be just relayed, have to be demodulated or not, or have to be demodulated and deencoded or not.