The white parts are firmer and can be used in a pan sooner but the green parts have a different texture and can get slimy if used too early in a recipe that involves pan frying. Most recipes will tell you which part to use.
Generally though the Green Parts are used for more of a garnish and are diced. The White Parts taste more onion like.
You can freeze Green Onions/Scallions but it will change the texture so its best to use them in stews, sauces or crock pot meals if they were frozen. I like to freeze the Green and White parts separately since some recipes call for only one or the other.
How to freeze Green Onions by HGTV Gardens.