Both are characterized, their genes are usually described and published, they are kept safe, they could be used as inoculum or to produce vaccine... Would it be correct to say a strain would be somehow a successful isolate ?
An isolate is a sample. It's this particular virus in this fridge, that was isolated from this, e.g., sputum sample, and cultured. A strain is more abstract -- it is a distinguishable, stable genetic variant of a species. An isolate may be identified as a particular strain of a particular species. That's how I and my colleagues use these terms, in any case, and how they're generally used in the literature. You can read more about this here and here
From the first reference (since it's behind a paywall)
An isolate may be defined as “a sample of biological material, especially a microorganism, that has been cultured for study” which is clear, perfectly acceptable and useable by virologists.
Although there is no official definition of a strain, the strain concept is widely used and a de facto definition states “strains are viruses that belong to the same species and differ in having stable and heritable biological, serological, and/or molecular characters”.