Cats are not especially good at making their distress obvious. Where a dog's stress tends to be loud and visible, a cat's is often quiet, gradual, and easy to put down to "just being a cat." Knowing the actual signs is the useful bit.
Acute stress: the signs are physical
International Cat Care describes a fairly recognisable set of physical signs when a cat is acutely stressed in the moment: freezing, shaking, a tense, crouched posture, dilated pupils, flattened ears, a tucked tail, and in more extreme cases an arched back with fur standing on end, or involuntary elimination. These are short-term, situational responses, a vet visit, a car journey, an unfamiliar dog in the garden, rather than an ongoing state.
Chronic stress: the signs are behavioural, and easier to miss
This is the harder category, because chronic stress rarely announces itself. International Cat Care lists the changes to watch for: not eating, grooming, or toileting as normal (in either direction, including over-eating), hiding more than usual, a heightened startle response to ordinary noises, and a cat becoming either more clingy or more withdrawn than it used to be. None of these look dramatic on any single day. They matter as a pattern, a change from how that particular cat normally behaves.
What tends to cause it
International Cat Care points to three common sources. Other cats, whether through resource competition or territorial tension, are one of the biggest. Owners themselves can be a source too, simply by wanting more contact or interaction than a cat is comfortable with at that moment. And the environment itself, particularly for indoor cats, if there aren't enough resources or hiding spaces to give a cat a genuine sense of control.
What helps
The practical guidance is to keep routines predictable, provide resources on the "one per cat, plus one extra, in different locations" principle (this applies to litter trays, feeding stations, and resting spots alike), and let a cat choose when it wants contact rather than initiating it on a fixed schedule. For indoor cats specifically, climbing opportunities and enrichment help address the environmental side.
When to see a vet
Chronic stress in cats isn't only a behavioural issue. International Cat Care specifically flags stress-related physical illness, feline idiopathic cystitis being the clearest example, as a reason to involve a vet rather than treating persistent signs as a purely behavioural problem to manage at home.
Source: Stress in Cats, International Cat Care.