it's been found that a protein of interest that binds at a particular pH in a weak ion exchanger
does not bind in a strong ionexchanger.both experiments were performed in similar conditions,and both the matrices were equilibriated properly with the same buffer,same amount of protein was loaded to both the columns.why should there be so huge a difference that a protein binds in a weak exchanger and does not do so in a strong ion exchanger??

.....thought someone who knows better would answer here. I have not done IC with proteins, but from my RP and GPC experience it could be guessed that either the pores are different or your protein has a different size (shape) in the two columns.
Again: it would be nice to hear about any further investigations into the cause of this.

Or the binding is not by ion exchange...

There are a number of possible explanations for your observation. For example, if you're working with an acidic protein at a pH that is higher than the isoelectric point of the protein but low enough to protonate the carboxylate groups in the weak cation exchange phase you might expect to see no retention on a strong cation exchange phase but might still see retention on a weak cation exchange phase. In the latter case the retention mechanism could be either hydrogen bonding or "HIC". An analogous situation can occur with a basic protein at suitably high pH when comparing a weak anion exchange to strong anion exchange. Can you tell me more about the specifics of your method and the columns you have used?