In the context of most discussions on this site, “confidence” is the probability that a guess is correct. For example:
I guess that a flipped coin will land heads. My confidence is 1⁄2, because I have arbitrarily picked 1 out of 2 possible outcomes.
I guess that, when a coin is flipped repeatedly, the ratio of heads will be close to half. My confidence is close to 1, because I know from experience that most coins are fair (and the law of large numbers).
“Confidence interval” is just confidence that something is within a certain range.
You should also be aware that in the context of frequentism (most scientific papers), these terms have different and somewhat confusing technical definitions.
In the context of most discussions on this site, “confidence” is the probability that a guess is correct. For example:
I guess that a flipped coin will land heads. My confidence is 1⁄2, because I have arbitrarily picked 1 out of 2 possible outcomes.
I guess that, when a coin is flipped repeatedly, the ratio of heads will be close to half. My confidence is close to 1, because I know from experience that most coins are fair (and the law of large numbers).
“Confidence interval” is just confidence that something is within a certain range.
You should also be aware that in the context of frequentism (most scientific papers), these terms have different and somewhat confusing technical definitions.