Is there some kind of official standard for signal measurements?
There is no standard for exactly what rise and fall times mean.  Even if there were, good documentation defines its terms.

In the case of rise and fall time of a digital signal, the appropriate thresholds depend on how the signal is intended to be received.  The first thing to look at are the levels are of the minimum guaranteed logic high and maximum guaranteed logic low.  For any specific receiver, these are the levels that matter.  Of course you need these levels to be guaranteed at the receiver end of whatever transmission line is between the sender and receiver, so there needs to be some margin beyond the min/max levels at the sender end.

If the spec is for something more general and various receivers could be used in the future to detect the signal, then you usually get more conservative.  Even receivers with Schmitt trigger (hysteresis) inputs usually have their min/max levels no wider than 20% and 80% of the supply.  In that case, you might specify rise and fall times between the 10% and 90% thresholds.

For analog signals, rise and fall times take on a whole different meaning.  These are often specified to settle within some minimum error of the final steady state.  If the signal needs to be accurate to within 1%, then it hasn't "settled" until it gets to within 1% of its final value.  You'd usually add some margin there too, since there are other sources of errors in the system.  You might specify "settled" as within &frac12;% of the final steady state value, for example.

Again, don't leave things like this open to interpretation.  Good specs include definitions for anything that matters that could be interpreted differently.