They are similar because they both have the definition of if A=B and B=C then A=C. They are different because since every parallel line is equal it shows that they do not exactly match up because of the transitive property of congruence.
In general, transitive property state that if a = b and b = c, then by transitivity, a = c.
In case of parallel lines, the transitive property of parallel lines states that if line 1 is parallel to line 2 and line 2 is parallel to line 3, then by transitivity, line 1 is parallel to line 3.
In case of congruent triangles, the transitive property of congruent triangles states that if triangle 1 is congruent to triangle 2 and triangle 2 is congruent to triangle 3, then by transitivity, triangle 1 is congruent to triangle 3.
Transitive property of parallel lines is similar to transitive property for congruent triangles in the sense, it gives a relation between three elements like three parallel lines an three congruent triangles.
The difference between them is when we talk about transitivity of congruent triangles we talk about equality, the three triangles are equal but no such thing follows for parallel lines.
