What is the "stimulus" that initially triggers an action potential?
There are several possible answers, which is partly why the sources you are reading are being vague: they are discussing the chain of events that happen after the initial depolarization, the source of which doesn't matter much for that chain of events.

Receptor potentials

Sensory receptors consist of some machinery that eventually lead to ion channels opening, often cation channels. This machinery can be direct, where a stimulus directly opens an ion channel, or it can me mediated through g-protein coupled receptors. There are many many examples, but one favorite toy example is the TRPV1 receptor, part of the "transient receptor potential" family.

TRPV1 channels open when exposed to high temperatures or chemical agonists like capsaicin (which gives chili peppers their 'heat').

There are mechanically gated channels in the inner ear that are stretched open as sound waves pass; there are G-protein coupled receptors in the retina that are activated in response to light - when they are activated, they close channels which reduces neurotransmitter release and therefore changes the amplitude of the post-synaptic polarization.

Ligand-gated ion channels

Synaptic transmission between neurons is often mediated by ion channels that are gated by neurotransmitters. A presynaptic cell releases a neurotransmitter, for example glutamate, and that neurotransmitter binds glutamate receptors on the post-synaptic cell, for example AMPA receptors. These receptors are non-specific cation channels, and when they open sodium comes in and depolarizes the cell. Other neurotransmitters, including inhibitory ones, work a similar way.

Gap junctions/eletrical synapses

Although they only occur between particular populations of neurons in mammalian nervous systems (for example, some inhibitory networks in the brain and between cardiac myocytes), some cells are coupled through channels that allow ions to pass between cells. Therefore, depolarization in one cell can be transmitted by ions flowing through that gap junction and begin to depolarize the adjacent cell.

Intrinsic conductances

It doesn't really apply in the context of a "stimulus" but in some types of cell there are intrinsic conductances that can bring a cell to threshold and trigger an action potential. One example would be in the pacemaker cells of the sinoatrial node that initiate cardiac contractions.