A ical result of Miyanishi-Sugie and Keel-M$\rm {}^c$Kernan asserts that for smooth affine surfaces, $\mathbb {A}^{1}$-uniruledness is equivalent to $\mathbb {A}^{1}$-ruledness, both properties being in fact equivalent to the negativity of the logarithmic Kodaira dimension. Here we show in contrast that starting from dimension three, there exist smooth affine varieties which are $\mathbb {A}^{1}$-uniruled but not $\mathbb {A}^{1}$-ruled.