Intersection[tes1, tes2] 

{{0, 2}, {1, 2}}

Select[tes1, MemberQ[tes2, #] &] 

{{1, 2}, {0, 2}}

Intersection[tes1, tes2] 

{{0, 2}, {1, 2}}

Select[tes1, MemberQ[tes2, #] &] 

{{1, 2}, {0, 2}}

Update: Using the lists Downn and Upp from OP's link:

Intersection[Downn, Upp] 

{{4.5, 2.59808}, {7.5, 9.52628}, {12., 3.4641}, {15., 10.3923}}

ListPlot[{Downn, Upp, Intersection[Downn, Upp]}, PlotStyle -> {Directive[Opacity[.7], AbsolutePointSize[5], Green], Directive[Opacity[.7], AbsolutePointSize[5], Blue], Directive[Opacity[.7], AbsolutePointSize[10], Red]}, ImageSize -> Large, PlotLabel -> Row[{"intersection = ", ToString@Intersection[Downn, Upp]}]] 

$Version 

"12.0.0 for Linux x86 (64-bit) (April 7, 2019)"