This is an educational overview, not a diagnostic tool. Only a clinician can diagnose your headaches.
Headache disorders are formally classified by the International Classification of Headache Disorders, third edition, known as ICHD-3, which is published by the International Headache Society. It is the reference clinicians actually reach for. A useful first split is between primary headaches, where the headache is the disease itself, and secondary headaches, where the pain is a symptom of something else. The three types below are all primary. Here is how they differ once you look at their defined features rather than the folk descriptions.
Migraine
Under ICHD-3, a diagnosis of migraine without aura calls for at least five attacks that each last somewhere between 4 and 72 hours if untreated. The pain has to carry at least two of four features, meaning it is one-sided, or pulsating, or moderate to severe, or made worse by routine physical activity. On top of that, the attack has to bring either nausea, with or without vomiting, or sensitivity to both light and sound. Migraine with aura is scored a little differently, since the aura itself is diagnostic, so only two attacks are needed. Aura is usually visual but can be sensory or affect speech, and it typically develops gradually and resolves within an hour.
A quick bedside shorthand that clinicians sometimes use is POUND, which stands for Pulsating, duration of One day (the 4 to 72 hour window), Unilateral, Nausea, and Disabling intensity. The more of those that fit, the more migraine looks likely.
It is also worth knowing the episodic versus chronic distinction. When migraine or headache is present on 15 or more days a month for more than three months, it is considered chronic, which changes how clinicians think about prevention.
Tension-type headache
This is the most common headache overall, and its profile is almost the mirror image of migraine. It is usually felt on both sides, with a pressing or tightening quality, the classic band around the head. Intensity tends to be mild to moderate. Crucially, it is not typically made worse by ordinary activity, and it usually lacks the nausea and the light and sound sensitivity that define a migraine attack. Because it is milder, people often manage it without ever seeing a clinician, though frequent episodes are still worth attention.
Cluster headache
Uncommon, and severe. The attacks are strictly one-sided and centre around or behind the eye. Individual attacks last from about 15 minutes to 3 hours if untreated, and they arrive in bouts, recurring from every other day up to eight times a day for weeks at a stretch. What sets them apart is the set of same-side autonomic signs that come along, such as a tearing or reddened eye, a congested or running nostril, or a drooping eyelid (Mayo Clinic). People are also typically restless during a cluster attack, pacing rather than lying still, which is a helpful contrast with migraine.
Two traps worth flagging
First, the so-called sinus headache. Recurrent "sinus headaches" that show up without any actual infection are frequently migraine in disguise, because migraine readily produces facial pressure and nasal symptoms. Getting the label right is not pedantry, since the treatments genuinely differ.
Second, medication-overuse headache. Using acute pain relief too often, more than about 10 to 15 days a month depending on the drug, can paradoxically drive a near-daily headache of its own. It is common, easily missed, and improves when the overused medication is carefully reduced with guidance.
The criteria above are summarised from ICHD-3 and from Nature Reviews Disease Primers. None of it substitutes for an actual clinical assessment, which can weigh your full history in a way a checklist never will.