Basically yes, but also no, not really.
With common words like realise or organise, that’s basically the case. American English will tend to use the -ize ending in these cases, and British English will often use -ise. In British English though, it’s also possible, if less common, to use -ize: it’s actually quite common to see this spelling in 18th- and 19th-century British writing.
OK, that’s fine, easy enough to remember. Except there’s just a little more to it than that…
Realise/Realize, Organise/Organize… fine.
So what about these words, then… excise, suprise, promise, compromise, exercise, disguise? Can they also be spelled with a Z? Well, let’s try it and see what they look like…
excize, suprize, promize, compromize, exercize, disguize
Oh, they look wrong, don’t they!? OK, so we certainly can’t spell those words with a Z. Why not though? They look and sound the same as all those other -ise verbs, don’t they? They do, but the key thing here is how the words are formed.
With words that can be spelled either way, -ise/-ize basically functions as a suffix, added to an existing word or word root. Real-, organ-, final-… makes sense, doesn’t it? Take away those last three letters and you can still figure out the rough meaning of the word. Adding -ise/ize just tells you that the word’s a verb.
What about the words that have to end in -ise? Let’s try removing those last three letters from some such words:
disgu, comprom, exc, exerc, inc, pr, surp…
It doesn’t work, does it? And that’s because the -ise of those words is part of a pre-exising root: guise (external form, appearance), prise (take), cise (cutting). These are long-existing forms, often from Latin, within which the S has long been established. Adding -ise/ize to create a verb, on the other hand, is a fairly recent development, and as the meaning is clear enough from the part of the word before -ise/ize, using Z doesn’t really matter.
Fascinating, isn’t it!?
So how do you know if you can change the spelling or not? Just take away those last three letters, and if you’ve got something that looks like an existing English word, you can change the spelling.
Or, simply always use -ise, and you’ll probably always be right!