The actual distribution is an

exponential distribution, with lambda=1/600s (assuming difficulty is properly adjusted to the actual hashrate). This follows from the fact that block mining is a Poisson process (every fraction of time has the same, independent, chance for having an event).

Note that this is an idealized assumption: network delays cause the seconds immediately after a new block have a lower chance for producing a valid non-stale block. Also, I'm talking about actual block creation times, and not the times reported in their timestamps. Certain pools fiddle with these timestamps to increase the time work remain valid - they can, but that probably means the distribution is different when looking at timestamps (for example, it can be negative).

In summary, under idealized assumptions, the shape stays identical.