If two lines have the same gradient, then this means they are travelling in the same direction. Lines travelling in the same direction will never touch or cross each other even if extended to infinity. Lines with such a property are called "parallel lines." This is assuming they are not just exactly the same line.
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parallel lines
They are called skew lines.
these lines are called intersecting lines
They could be lines with the same gradient (or slope).
They are parallel lines