You distinguish between noise and signal by understanding your signal - you should have some idea what it will look like.
Alternatively, some "noise" sources are well known so that you know what they look like and can exclude them from the things that might be a signal.
In your case, you have a signal with some known characteristics meeting up with an interference source with known characteristics.
Start with the ECG signal. It has known characterstics. The signal is from an electrocardiogram. It represents heart beats.
What do you know about heart beats?
The most obvious thing is that they are relatively slow. They occur a little more than once per second. Once per second is a frequency of 1 Hz.
Look at your ECG signal plot. You say the sampling rate is 600 samples per second. What part of your signal repeats approximately once per second (every 600 data points or so?) The big spikes. Those are your heart beats.
You had eliminated the big spikes because you thought they were noise and that the constant waves were the signal.
Take a look at the constant wave. It repeats dozens of times in a second. It that were your heart beat, it would sound like a constant hum. You'd have a pulse of over 360 beats per minute.
Your FFT tells you more about the interference. There is a vertical line at 60 Hz. That's the frequency of the AC power as used in the United States - that's what comes out of the power outlets in your home.
You can eliminate the 60Hz as your signal. It is way too fast for a heart beat, and is a common source of interference. In Europe or other parts of the world, 50Hz is more common because they use a 50Hz power line network.
You can also eliminate the 120 Hz and 180 Hz components of the FFT. They are even faster, and they are related to the 60Hz power line frequency.
Given that this is an ECG signal, you can also compare your signal to a picture of someone else's ECG.
There's an image here that shows what an ECG signal looks like.
Here's the image:
- A = ECG with noise and 60Hz interference
- B = ECG with noise
- C = Clean ECG
A looks a lot like your ECG signal. If you clean it up, you get something like C.
You can tell the signal from the noise by either knowing what your signal looks like and picking out that shape, or by knowing what the inteference looks like and ignoring that shape. Either way, you have to know something about your signals to separate them.