What is the conditional mood of verbs?
Very few languages, if any, make a grammatical distinction between "conditional" and "subjunctive".
In every language I have ever studied which marks conditional differently than indicative on the verb, conditional ("If you X, then I Y") is marked by the subjunctive forms of the verb. Conditional is a subset of the situations in which you use subjunctive. Different grammatical traditions might call the subjunctive forms "conditional" or "subjunctive" or "irrealis".