Trans influence is related to the sigma donor ability of the ligand and it is manifested in the elongation/shortening of the bond trans to the ligand and, consequently, in the destabilization of the reactant.
Trans effect is, however, a kinetic phenomenon; to get a large trans effect, i.e. small reaction barrier in the SN reaction, you can destabilize the reactant and/or stabilize the transition state.
Obviously the two phenomena are related in the reactant destabilization, but even if you have weak destabilization of the reactant you can have still fast reaction, i.e. low barrier - large trans effect, if you stabilize the TS. This is what happening in the title ligands; for good pi acids, such as olefins or cyanide pi-backdonation significantly stabilizes the (typically) trigonal bipyramidal TS, reducing the barrier and might cause even larger trans effect than strong sigma donors without backbonding ability.
You can find a simple description of this topic in the introduction of this paper:
It is rare, but not unusual that trans influence and trans effect are unrelated. A relevant instance can be found in an old paper by Wendt at al. in Dalton 1997 page 4752.
As Pinter properly points out, the two phenomena have different origins. Altough these topics have been addressed in countless papers, we think that some points need further investigation. According to our studies, we believe that trans and cis influences are related to the charge of the donor atoms and to the amount of charge transfer from the donor to the acceptor. Thus the trans influence can be described in terms of competition between the charges on the two trans donor atoms. On the other hand high cis influence is displayed by ligands whose donor atoms possesses a (relatively) high negative charge.
Cyanid is having high trans directing character, since it is lying at high end of trans effect series, where the trans directing character depends the nature of pi bonding ligand.the ligand which will form metal ligand pi bonding very easily will have high trans directing character.the cyanid is more easily form metal ligand pi bonding,which facilitate to incoming ligand to occupy position trans to its.Thus cyanid is having high trans effect.
Trans directing character depends upon nature of ligand attached to central metal ion. Since cyanid is pi bonding ligand ,having vacant pi orbital,which can easily form metal ligand pi bonding. In trans effect series cyanid is lying at high end of series,and having ability to form metal ligand pi bond more easily, thus ligand which form metal ligand pi bond more easily, have high trans effect or high trans directing character .juneja