The 3 signals differ considerably: The EMG signal (potential difference between 2 electrodes) calculates the sum of action potentials delivered at the motor endplate in regard to the underlining muscle fibers. ECG is used to record the electrical activity of the heart from different angles to identify and locate pathology. The EEG is an electrophysiological method to record electrical activity of the brain. As the source of signal differed (muscle/heart/brain) these signals have very view in common.
See: Reilly, Lee (2010) Electrograms (ECG, EEG, EMG, EOG)
One of the main differences between them is their peak frequencies. We determine their sampling frequencies accordingly. Surface EMG is mostly recorded between 20-500 Hz (~100 Hz is its peak frequency). ECG is actually a specialized surface EMG. We mostly investigate ECG with frequencies less than 150 Hz, and EEG even less, even though high sampling rate is extremely recommended (at least twice the maximum frequency). Using filters, we can separate those signals arising from heart or muscle. Besides the frequencies, another unique property is the electrode placement during recording, which is mentioned by Ramona already.
For EMG and EEG; you can check following articles;
Article EEG-like signals can be synthesized from surface representat...
Article Interference of tonic muscle activity on the EEG: A single m...
You can refer to the book: Biomedical signal analysis by Rangaraj M Rangayyan. This book gives a clear description and differentiation between basic physiological signals such as ECG, EEG, EMG, and EOG. Though these signals are arising from various parts of the body, they have inter-relationships, because of the mutual relation between these systems. To understand the characteristics of the signal, it is mandatory to examine the underlying mechanism of these systems. Thank you.