There are lots of voltage and current ratings for parts.
There's usually a current rating per pin on connectors, (as well as a voltage rating which does not refer to the same thing). On ICs, there is usually a current and voltage rating on IO ports when used as an output or an input (how much it can source or sink - current - and the maximum voltage permitted on the pin as an input usually). There are many, many other voltage and current ratings (to say nothing of power ratings and derating information).
In many (most?) cases, the two are not referring to the same thing.
Your post is mixing things apparently out of context, and in electronics, context can be everything.
Get a specific part and ask about it - all will be explained by the usenet denizens :)