The 20=30 and 1=-10 is interesting and would like to see it in use. According to what I have seen in PHB and DMG a "20" is always a hit and a "1" is always miss. The optional rule of rolling a second 20 and it being a automatic kill is as I said optional and can cause a lot of problems.
This is according to SRD "Critical Hits"
When a character makes an attack roll and gets a natural 20, the character hits regardless of the target's AC, and the character has scored a threat. The hit might be a critical hit (or "crit"). To find out if it's a critical hit, the character immediately makes a critical roll — another attack roll with all the same modifiers as the attack roll the character just made. If the critical roll also results in a hit against the target's AC, the character's original hit is a critical hit. If the critical roll is a miss, then the character's hit is just a regular hit.
A critical hit means that the attacker rolls for damage more than once, as indicated by the weapon description for the weapon that scored the threat, with all the attacker's usual bonuses, and add the rolls together to get total damage.
Exception: Bonus damage represented as extra dice is not multiplied when a character score a critical hit.
But there is a section on combat basics that says "BASIC TASK RESOLUTION SYSTEM
These rules assume a standardized system for determining the success or failure of any given task. That system is:
d20 + Modifiers vs. Target Number
The Modifiers and Target Number are determined by the type of task.
If the result of the d20 roll + the Modifiers equals or exceeds the Target Number, the test is successful. Any other result is a failure.
A "natural 20" on the die roll is not an automatic success. A "natural 1" on the die roll is not an automatic failure.
This is for skills i believe and not combat so there is your difference you may have seen.