Yes, they are the same; no, there's no difference in grammar and use. In American English, the 'ize' form is always used. In British English, the 'ise' form is traditionally used. However, the 'ize' form is also common in British English, and becoming more so. In other words, the 'ise' form looks strange to American English users, while both forms look fine to British English users. To make life easy for yourself and keep everyone happy in an international context, I'd recommend you use the more universally acceptable 'ize' form.

It's just a US/UK English difference in spelling. Most long words which end in -ize can also be spelt ending in -ise in UK English. If you want to avoid worrying about the issue in your writing, just use -ize because it is acceptable everywhere. Be careful of short words like "wise" and "size" which have fixed spellings and do not vary in spelling between the US and the UK.

Many of these differences are because of the difference between American and British English. the ending -ise is used by some British people, while -ize is used by Americans (and some British people). Generally, words are spelt in American much closer to how they sound. A very common set of examples is the omission of 'u' from words such as colour, honour and armour.