The -se forms descend from the Latin imperfect subjunctive. It is more common in some countries (like Spain), and has a higher frequency in writing than in speech.
The -ra forms descend from the simple (or synthetic) pluperfect indicative such that where as now you might see a sentence like No quería café porque ya había tomado té, in the past, would have seen No quería café porque ya tomara té. The evidence of this past is seen in other modern-day Romance languages (Portuguese: não queria café porque já tomara chá, Asturian: nun quería café porque yá tomara té).
In most modern usage, there is no difference in the subjunctive, other than the -se forms perhaps being perceived as of a slightly higher register. It is not uncommon to hear people in a single phrase alternate forms: El profesor dijo que el alumno comprase el libro de la librería, leyera el capítulo 2, hiciese la tarea al final del capítulo, y se la entregara al principio de la siguiente clase.
Using the -ra forms in the indicative is highly inadvisable, although journalists do tend to use it every now and then and every now and then you might see it in an academic paper or poetry, and (IIRC) the only other rationale the RAE gives for using it is if you're from Galicia/Asturias where the indicative form still enjoys use thanks to influence from Galician/Asturian, I'll check my Gramática later and update. That said, when you use -ra for the indicative, you may not alternate with -se, because it has never had any indicative value. Hence an expression like quisiera un café (which is not actually subjuntive, it's había querido un café) may not be recast as quisiese un café.