Why does TensorContract differ from reshaped arrays in Mathematica?

Question

I am recently trying to perform tensor calculations with Mathematica as I came across problems like these:

Given two tensors M,N (here matrices), I want to compute something like

m = RandomReal[{}, {2, 4}];
n = RandomReal[{}, {2, 4}];
TensorContract[TensorProduct[m, n], {2, 4}]
={{1.2092, 0.892127}, {0.497884, 0.14624}}

i.e. the contraction w.r.t. the second index respectively. But whenever I try to alternatively compute

m . Transpose[n, {2, 1}]
={{1.2092, 0.892127}, {0.497884, 0.14624}}

it looks like the same value but still the difference is non-vanishing:

TensorContract[TensorProduct[m, n], {2, 4}] - m . Transpose[n, {2, 1}]
={{0., 0.}, {-5.55112*10^-17, -2.77556*10^-17}}

I would be very thankful if some of you guys would try and help me understand why there is a difference between these two approaches, maybe what they have to do with MachinePrecision and perhaps what value is more accurate. Any help is appreciated!