What's the difference between large and small scale signals
It would help if you provided a context where these terms are used.  Most mentions of "small signal" I have seen have been in opamp datasheets.  For example, you might see a small signal gain spec.  That is the output change divided by the input change where the output doesn't have to move much.  It is therefore not limited by the slew rate or hitting the clipping limits, which are different issues with their own specs.

For example, a opamp might have a open loop small signal gain of 100k.  That means a 10 &micro;V differential input change will result in a 1 V output change.  However, a 1 V differential input change might only result in a 10 V output change because the output has reached the supply limit and can't drive farther.  It certainly can't reach 100 kV like the small signal gain would suggest.