The default type for tangents is Auto. See Tangents menu.
If you selected a key on a curve, only the curve segments before and after the current key acquire the specified tangent type.
If you want to set the tangent type for a curve segment before or after a key, use Tangents > In Tangent > (before) or Tangents > Out Tangent > (after) in the Graph Editor. See In Tangent and Out Tangent.
To set the tangent’s level of influence
Non-weighted tangents have short tangent handles that only control the angle of the tangent.
Weighted tangents have long tangent handles that control the angle and weight of the tangent. Weighted tangents provide finer control over your animation curves.
Tangent weights dictate the amount of influence a tangent has over a curve segment. See Non-Weighted and Weighted Tangents.
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