I haven't read the holy liberator in awhile, but I'd say that the difference is that one belongs to an organization and has responsibilites to them, while the other is a free spirit. I refuse to believe that a Paladin would be forced to put themselves in danger before engaging in battle. I don't like that concept at all. By all means feel free to do if you're playing one, but you don't have to. I like Xoad the Slayer in RttToEE, he's my ideal Paladin. Go where the god tells you, slay evil, etc. Follow orders when given by a superior, but be a mean, nasty ball of holy fury when fighting.
If an opponent trips and falls use the opportunity to kill him, don't hand him his weapon and help him up.
Ambushing is on a case to case basis I guess. Standing around using detect evil shooting anyone that detects is one thing. Recognizing a known foe and laying in wait is something else.
It's hard to know because the real world is relative, DnD is absolute's. I respect other peoples opinions when they're the DM, but I don't like to be straightjacketed and get toyed with as a player.
When I started DMing a friend told me about one DM who wouldn't let Paladins fight unless they were swung at first, so the rogue would mercilessly tease him and mock him constantly and he couldn't do anything without violating alignment. Anyways, the DM put him in an odd spot and things like that prevent players from being Paladins when they play. I decided I didn't want to be like that.
In my game one of the players accidentally contacted lycanthropy, and was heading to get it cured before the next full moon. He'd already turned once so he knew he had it. Anyways, a couple Paladins and a Cleric (with a lycanthrope turning domain) were dispatched to find them since a farmer saw him eating a few chickens. The PC's were sleeping with one guy on watch. The Paladins rode into camp on horseback in the middle of the night followed by the Cleric. Swords were pointed, crossbows aimed and the PC was told to give up or die. They were all unarmed and unarmoed and really had no option. If they'd have tried something they'd have been in trouble. That's an ambush, but the PC's had a chance the Paladins didn't just shoot the wererat while he slept. I don't have hard and fast rules, but ambushing a cleric of your arch enemy religion is something I'd allow.
Hard to say really, you need to be a supurb DM to not screw up...

Not saying I am one, but I'd rather err on PC flexibility. The line is hazy, but cross too far into evil acts and people will know it. Be overly harsh and nobody will play paladins because they're less effective fighting evil then other people. Paladins should be the MOST effective class at killing evil and preserving good by virtue of a good sword-arm. 500 miles from nowhere and you get ambushed by Orcs and cast sleep? Kill em I say.