depends on what type of hardware you are refering to.
there are one-shot programmable IC's that can 'burned' to provide a set logical algorithm. ( like the ones used by the cable guys for storing the descrambler code )
there are also more 'general pupose' types that can handle instruction like a processor. ( DSP's like what is used in alot of software modems, toys, appliances, etc. )
my guess would be you are refering to a "custom" chip as one that has been 'burned' for a specific task, and universal chip as more processor oriented like DSP's (digital signal processors)