It's impossible to give a simple answer to this very complex question. If you look up these two terms in bilingual dictionaries you get the same answer for each: editor or editor in chief. This is true of the Oxford, for example. In Collins it gives "editor" for "director" and "editor-in-chief" for "jefe de redacción", but that's no help at all, because in English "editor" and "editor in chief" (and also "executive editor" and "chief editor") are different terms for exactly the same thing: the overall editorial head of a newspaper. Some papers distinguish them, but on an individual basis, so there's no systematic hierarchy in these terms applicable across the board. (By the way, there is no consensus on whether to hyphenate "editor[-]in[-]chief".)

The trouble is that these terms are not used the same way in every publication. In Spanish, some newspapers have a "director" at the top, some have a "jefe de redacción" but no "director", and some have both. Most major newspapers in Spain are headed editorially by the "director" (El País, El Mundo, ABC, La Razón...). Most British papers are headed by a figure called simply the "Editor". The term "editor in chief" is not common in the UK in newspapers, but it is more widely used in the US. So there is a basic equivalence between "director" and "editor/editor in chief".

If a Spanish-language newspaper has a person called the "jefe de redacción" but nobody called the "director", then the "jefe de redacción" is the editor or editor in chief.

But when a paper has both positions, "director" is senior to "jefe de redacción". How to handle this in translation will depend on the case.

Sometimes there is a single "director" and a single "jefe de redaccion" below him/her. In that case, to distinguish them you can call the former the "editor" (or "editor in chief") and the latter the "managing editor". The latter, at least in the US, is a figure who supervises the editorial department and reports to the editor (in chief): a more hands-on role.
http://work.chron.com/difference-between-editor-chief-managi...

In other cases, a paper can have a "director" and several "jefes de redacción" below him/her. This is true of El País in Spain, for example. In this case, the equivalent in English would depend on the particular case. These "jefes de redacción" are the heads of particular sections of the overall operation. They could be the heads of the news department (the news editor), the features department (features editor), and so on, or they can be overall editors of particular editions: the editor of the Madrid edition, the Seville edition, or whatever. The translation would have to be adapted to the circumstances; there is no single answer for this situation.

The key points to bear in mind are:
1. Each of these terms, in isolation, can be translated as "editor".
2. When the terms are found together and you need to distinguish them, the key point is that the "director" is always more senior than the "jefe de redacción".

Generally speaking "deputy editor" is not the way to go for "jefe de redacción". The deputy editor is the subdirector. A "jefe de redacción" is the overall head, not a deputy, of some aspect of a newspaper's operation: either strictly the editorial department (as opposed to the whole newspaper) or a particular section or edition.