An isosceles triangle has two equal sides.
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An isosceles triangle has three sides, two of which are exactly equal in length.
Either a scalene triangle or an isosceles triangle.
An isosceles triangle is any triangle with two sides of equal length.
An isosceles triangle is any triangle with at least two sides of equal length. Logically, an isosceles triangle also has at least two angles of equal size. An equilateral triangle is a triangle with three equal sides and three equal angles (all of which are 60 degrees). Since it has at least two equal sides then it is therefore also an isosceles triangle. This is no different to the way in which a square is also a rectangle, or a circle is also an ellipse. They are simply special cases of the general case.
Using the traditional definitions, a triangle that has two equal sides (and angles) is an isosceles triangle and one with three equal sides (and angles) is an equilateral triangle. However, some mathematicians define an isosceles triangle as any triangle having at least two equal sides, which is what you are describing.