Output current vs Supply current
You are looking at the "Limiting Values" table, also known as "Absolute Maximum Rating"  The part may be damaged if you exceed these ratings.  You should never operate the part at the ratings given in that table.

You should look at the "Recommended Operating Conditions" and other tables to find the normal supply voltage and other normal operating conditions.

Under Recommended Operating conditions, you will see that the 74HC08 will operate correctly with a supply voltage between 2 and 6 volts, while the 74HCT08 requires 4.5 to 5.5 volts, and the output current in either case should be limited to 5 mA or so.  The actual power supply current for both types is 40 uA, plus any current delivered to the outputs.