If it's the typical elite-status perk, the usual rule is that you need to be flying that alliance that day. In other words, if I'm flying MCI-ORD-LHR entirely on AA, I can't show up at a UA lounge in ORD with Star Gold status and get in. I would imagine that they'd happily sell me a daypass if I was so inclined to buy it, but I've never actually tested this.

When you say credit card access, it varies. If you're talking about the high-annual-fee cards that basically build the lounge membership into the fee of the card, I would assume that you're treated as a full member of the club and could enter it anytime. (Disclaimer: I don't hold these credit cards so I don't know if this is true, but for $450/yr., it had better be!) If you're talking about the daypasses that come with some of the "normal" airline cards (like the ones I get with the US Airways Mastercard), I think there's some same-day-travel language in the fine print.