Need critical help: How to detect and distinguish two very similar looking signals?
As Conrad pointed out, a correlator is probably your best bet.

The correlation of a signal with itself (also known as its self-similarity) is larger than its correlation with any other signal (except for a constant factor related to the signals' energy).

In your case, you would implement two correlators, one for Signal 1 and one for Signal 2. Then, you'd look for one of the correlators' output to be larger than a certain threshold. You may have to run a few tests to determine the threshold.

One nice benefit of using correlation is that you don't need to synchronize your time window to the signals. Just be sure to accumulate the correlation calculations from one time window to the next.