I think there was a related discussion about this topic a while back, but anyway....
Standard Temperature and Pressure (STP) is considered to be 0°C and 1 bar. Because of the fact that STP requires a refrigerator to exist, many people will mention Standard Ambient Temperature and Pressure (SATP), which is 25°C and 1 bar. This should be, hopefully, the conditions at your typical lab bench. :)
A standard state is different. It's a set of conditions which allows for fairly easy comparisons of thermodynamic properties (and calculations thereof). While the standard state quantities one sees in textbooks for secondary level and introductory university level chemistry are for STP and/or SATP, they're not the only ones by any means. For example, if one gets into geochemistry, you're going to need standard state values at pressures nowhere near those values for doing your work. There's also an idealization of either gas or solution behavior (e.g., ideal gas behavior or infinite dilution limit).