Ils sont des rois

is pronounced with an S like in snakes, but

Ils ont des rois

is pronounced like a Z, like in maze. When doing the link between two words in french, if the last letter is an “s”, the sound will always be “z”.

First things first,

Ils sont des rois

This is not a very correct way of putting it. You should prefer:

Ce sont des rois

Now, you do have a point. How could you differentiate:

Ils sont pris au piège (they are trapped)

Ils ont pris au piège des lapins (they trapped some rabbits)

As said by Lyzvaleska, the first indice is the z sound when pronouncing: Il'z ont. Ils will always connect to the following vowel if there is one.

But another tips is the complement d’object direct (les lapins) which is required when using Ils ont and absent when using Ils sont.