What is the difference between an English pint glass and an Irish pint glass?

A pint glass is a drinking vessel made to hold either a British ("imperial") pint of 20 imperial fluid ounces (570 mL) or an American pint of 16 U.S. fluid ounces (470 mL). These glasses are used predominately to serve beer.

In Australia it is common for "Irish pubs" to serve in 570 mL (20.06 imp fl oz; 19.27 U.S. fl oz) glasses whereas most other pubs will generally serve in 425 mL (15 imp fl oz; 14 U.S. fl oz) glasses.

The Republic of Ireland also uses 570 mL 1 pint glasses, where legal metrology marks are used to show that a glass has passed inspection by the National Standards Authority of Ireland, a state-run body who enforce a number of standard rulings.

https://en.wikipedia.org/wiki/Pint_glass

A British (not English) pint glass holds more than a pint but has a mark for the top of the liquid to ensure that a pint of beer (or cider) is being served and to allow for the frothy head to be present. Most glasses for pub use have this mark (and usually a half-pint mark too) and an official mark to certify this. (Older type glasses holding an exact pint are found in domestic use. Pewter tankards hold a pint normally, but Baloo has found two of his to be a fraction short, which is why they are confined to the house.) I don't know whether or not the Irish ones have the head space. If they do, the only difference will be the standards mark.

The UK also has half pint and allegedly third pint glasses, but I've never seen a third pint, don't know anyone who would use one and can't see the point.

I thought the glasses were shaped differently?

Pint glasses here can be of many shapes. Quite a few are branded and shaped for a specific beer (but not always used just for it), top hats are very common, but ones with a swoosh out and in near the top are too. You can still get ones with handles in some pubs, but they're dearer to buy, so less common. (If I've not got a tankard with me, I prefer handled glasses.)