I was reading about the CLT and found something that I think people use interchangeably. On one hand I found that 68% of the means are 1 standard deviations from away and 95% are 2 std dev. On the other hand, if I take a look at the Z-table I found that 68% is approx 1 std dev whereas 95% is 1.96 std dev away.
Can someone clarify this please? Are these values of "std devs away" interchangeable? Or better yet, what am I confusing?
Both are approximations, though the second is a very good one. The actual percentage of the area under the normal curve that is within two standard deviations of the mean is about $95.44\%$; the cutoff within which you get $95\%$ of the area is very close to $1.96$ standard deviations on each side of the mean.
The rule of thumb that says that about $68\%$ of the area is within one standard deviation, about $95\%$ is within two, and about $99.7\%$ is within three is just that: a rule of thumb. These are approximate numbers that are easy to remember.