What proportion of all strokes are ischaemic vs haemorrhagic?

As you correctly point out, strokes may be caused by two general mechanisms, both fortunately described by their names.

Ischaemic strokes are caused by arterial occlusion (e.g. by an embolus or a ruptured plaque which thromboses up).

Haemorrhagic strokes are caused by ruptured vessels. Leaking blood can compress and injure surrounding tissues, and can also cause a lack of blood to its usual supply areas downstream.

To answer your question then, ischaemic strokes in Western societies account for about 80% of all strokes, with haemorrhagic strokes making up the remainder.

This distinction is important, since if patients with ischaemic strokes can get intravenous thrombolysis within three hours (e.g. with the 'clot-buster' called recombinant tissue plasminogen activator), they tend to have a better outcome, provided there are no contraindications to this treatment. On the other hand, giving thrombolytic therapy to a patient with a haemorrhagic stroke could obviously kill them!

Although there are a few clinical guides to distinguishing which type of stroke the patient is having, they are unreliable, and the patient will need either a CT scan or an MRI to tell which type of stroke it is.