Current carrying capability of 30AWG
The current carrying capacity depends on the ambient temperature, the type of insulation and the number of wires bundled together in addition to the wire size. The highest capacity is obtained by using a single, un-insulated wire in the air. The table in your post appears to be for un-insulated wire in free air. You need to find a table for the insulation that you are using, the temperature that you estimate for your circuit, and the number of conductors that will be run in a bundle. You probably need to use a chassis wiring table because the wires will be run along a supporting surface rather than through the air or in a conduit.

There are many types of insulation, but only a few that would be common for 250 volts or less and sold in single-wire spools rather than cables of several wires in a sheath. The type of insulation and rated voltage and temperature for the wire should be stated in the catalog or web-site where you buy the wire.

Edit:
30 AWG wire does not have enough mechanical strength to be used for use in chassis wiring. It is normally found only in cables that have several wires with a strong outer covering. 30 AWG magnet wire is used for coils that are wound in motors and solenoids with additional varnish, covering material or other measures to protect the strands of wire from vibration and breakage. For chassis wiring, you should use 20 or 22 AWG as a minimum size. You may need to size the wire based on voltage drop rather than insulation temperature limits.

Edit 2:
Also look at the list of related questions that should come up on the right side of your screen. For example: Determining maximum current through 18 gauge wire in robot arm

Edit 3 - Chassis Wiring vs. Power Transmission

Here is a link to a wire and cable manufacturer that states that "Power transmission wiring refers to any wiring that is bundled together." So my assumption about overhead power transmission lines is incorrect. That table should be a good for any project wiring using the "Chassis Wiring" column for single wires separated from other wires and the "Power Transmission" column for bundles of wires and cables. It is likely good for the most common types of wire and usual temperature range for electronic projects.