Is there any way to differentiate between impulses? I have a set of signals consisting of impulses at different instant of time i.e. its not a continuous signal. What I want is a mathematically intuitive way to distinguish between any two such signals?

I understand that the time of occurrence of impulses can be used to differentiate between the impulses. But what I need is like a single number that gives a measure of how different two impulse signals are for instance it could be some property of the signal that would be different for any two signals.

Just an additional info the signals are defined on finite duration. I don't know if that info is needed or redundant.

I don't come from a signal processing background so this question could be wrong. Also if I have tagged it wrongly please modify it.

An example of 2 signals would be:

[0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1]
[0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1]
If you are looking at vectors $\mathbf x$ and $\mathbf y$
(presumably of the same length) in which the entries are
mostly $0$s and


with occasional $1$s (unit impulses), a good measure of the difference
between the vectors is the Hamming distance between them, that is, the
number of samples in which $\mathbf x$ and $\mathbf y$ differ
with occasional non-zero entries (impulses of different amplitudes),
then we need to distinguish between impulses of different amplitudes
but the same location. If we use Hamming distance, then the measure
of the difference between
$$\cdots \quad 0\quad 0 \quad 0 \quad 1 \quad 0 \quad 0\quad 0\quad \cdots$$
$$\cdots \quad 0\quad 0 \quad 0 \quad 2 \quad 0 \quad 0\quad 0\quad \cdots$$
and
$$\cdots \quad 0\quad 0 \quad 0 \quad 1 \quad 0 \quad 0\quad 0\quad \cdots$$
$$\cdots \quad 0\quad 0 \quad 0 \quad 9 \quad 0 \quad 0\quad 0\quad \cdots$$
is the same which is not quite capturing our intuition that the two pairs
are more different than the Hamming distance is telling us. Possibilities 
to consider in this case are
$$\sum_{i=1}^n |x_i - y_i|,\quad   \sum_{i=1}^n |x_i - y_i|^2,\quad 
\mathrm{or}\quad \sqrt{\sum_{i=1}^n |x_i - y_i|^2}.$$
The last quantity is the Euclidean distance between the vectors. Which
measure you want to use depends on how much the measure captures the
features relevant to your application.