The word "tense" is somewhat abused by language teachers. Technically, it refers only to the time of a verb's action, independently of its mood (See also Temporality).
However, when it comes to conjugating verbs, the term "tense" usually refers to a specific combination of: Tense + Mood (+ sometimes Aspect).
Therefore, when someone asks to conjugate in the "present tense", or Le Présent, they always mean Le Présent de l'Indicatif, i.e. "the present tense of the indicative mood".
If we refer to the present tense of another mood, we will mention the mood specifically:
Le Conditionnel Présent (or Le Présent du Conditionnel).
Vice versa, when the other tenses of that mood are very rarely used, we often use the mood alone to mean the present of that mood:
L'Impératif meaning L'Impératif Présent (or Présent de l'Impératif).