Behaves like a bidirectional length/2, same as:

?- length(L,3).
L = [_22942, _22948, _22954].

by generating lists of fresh variables as needed:

?- same_length(L,[0,1,2,3,4]).
L = [_7972, _7978, _7984, _7990, _7996].

?- same_length([0,1,2,3,4],R).
R = [_8914, _8920, _8926, _8932, _8938].

Non-determinism if both arguments are fresh:

?- same_length(L,R).

L = R, R = [] ;

L = [_10602],
R = [_10608] ;

L = [_10602, _11640],
R = [_10608, _11646] ;

L = [_10602, _11640, _12678],
R = [_10608, _11646, _12684]
...

Also works with "difference lists" (i.e. lists with still-unspecified tail):

?- L=[1,2,3|LT],R=[a,b|RT],same_length(L,R).

L = [1, 2, 3],
LT = [],
R = [a, b, _102],
RT = [_102] ;

L = [1, 2, 3, _1404],
LT = [_1404],
R = [a, b, _102, _1410],
RT = [_102, _1410] ;

L = [1, 2, 3, _1404, _3204],
LT = [_1404, _3204],
R = [a, b, _102, _1410, _3210],
RT = [_102, _1410, _3210] ;

L = [1, 2, 3, _1404, _3204, _5004],
LT = [_1404, _3204, _5004],
R = [a, b, _102, _1410, _3210, _5010],
RT = [_102, _1410, _3210, _5010]