"should the need arise" means you think it might happen "when the need arises" means you think it likely to happen For instance, you have a friend having relationship problems with someone and you want to offer support to them. You don't want to say: "When the need arises you can call me on the phone." That will make it seem like you expect them to have further problems. Instead you would be more supportive by saying: "Should the need arise you can call me on the phone." That means "IF you run into trouble, call me" and does not come off like you are presuming they will have problems.

"Should" and "when" have the same difference as "If" and "when". In actual practice, the two phrases would be considered to be the same. A strict interpretation, however, would interpret the first to be conditional. The second would be interpreted to mean that the need will definitely arise, we just don't know when.

Grammatically, they are different, as stated by fdmaxey. In practice though, these two are really the same.

Should the need arise: Gerek olursa. / Eğer ki gerek olursa. (ihtimal) When the need arises: Gerek olduğunda / Gerek olduğu zaman. (kesinlik)