Start by observing, not intervening
The commonest mistake is acting on a single sighting. Many healthy cats roam a familiar patch daily, visit several gardens, and accept food opportunistically despite having a full bowl at home, so a cat in your garden at lunchtime may be a pet conducting its rounds rather than an animal in trouble. Give the question a little time unless the cat is injured, in immediate danger, very young, or clearly distressed, in which case getting help comes first and classification can wait.
Read condition and behaviour as a set of clues
No single clue settles it, but the pattern usually does. A neighbour's pet typically carries good weight under the coat, has clean fur without heavy matting or flea dirt, intact ears and eyes, and a manner that is relaxed, demanding or mildly indignant around people. A collar, especially one that looks current and well fitting, is a strong suggestion of a home, although collars do get lost.
A stray or lost cat more often looks thin when you see it from above or feel ribs too easily if it allows touch, has a dull or unkempt coat, minor untreated injuries, and a wariness that does not soften over repeat sightings. Lost indoor cats can look especially rough and behave almost feral with fear despite having a home, which is why behaviour alone should not decide it either. Kittens alone outdoors, a cat crying persistently, or one that has started sleeping in your shed in all weathers are stronger signals that help is needed soon.
Ask the neighbourhood before you feed or remove
Photograph the cat and ask around in widening circles: immediate neighbours first, since the cat's home is often a few doors away, then local lost-and-found and community groups with the photo and the street area where it is appearing. Knock on doors if you can; plenty of owners, especially older ones, are not in online groups, and a two-minute conversation can end the mystery instantly.
A paper collar is the classic low-tech test for a friendly visitor. Write a polite note saying this cat visits you and asking an owner to call your number, attach it loosely with tape so it tears safely if snagged, and wait. If an owner rings, you have your answer. If the paper collar stays on untouched for days while the cat keeps sheltering with you, that silence is itself information pointing toward a cat without a home checking on it.
Be careful what feeding sets in motion
Offering a little food to build trust for identification is reasonable, but full regular feeding of a cat that may have a home creates problems: it can draw a pet away from its own house, complicate a medical diet you know nothing about, and make a merely curious visitor look stray by encouraging it to stay. If the cat seems hungry and thin, feed it and escalate your enquiries in parallel rather than waiting, but keep the distinction in mind while evidence is thin.
Decide based on the whole picture
Weigh it all together: condition, confidence, hours, responses to your enquiries, the paper collar result, and any chip scan. A plump, relaxed cat with an untouched routine and an owner who calls you is a neighbour. A deteriorating cat that nobody claims, that shelters in your outbuilding and depends on your food, needs rescue involvement, and the sooner the better before winter, illness or injury compounds the problem.
Local knowledge is usually what cracks these cases, because someone nearby almost always knows whose cat patrols which wall, and KinsLe's Circle of Love is built for exactly that, connecting your free account to nearby pet lovers who can recognise a regular, share a sighting, or confirm that a cat has been missing from their street.