Rees-Zammit’s hat-trick during the 43-19 Pool C victory over Georgia took him to five in the tournament, one behind France star Damian Penaud.
Adams, meanwhile, led the way in Japan four years ago, claiming seven tries and finishing one short of equalling the record for most touchdowns during one World Cup that is jointly held by Jonah Lomu, Bryan Habana and Julian Savea.
Rees-Zammit became the seventh Welshman to score three tries in a World Cup game after Adams, Glen Webbe, Ieuan Evans, Gareth Thomas, Scott Williams and Cory Allen.
It was another exhibition of the 22-year-old’s dazzling finishing skills and why he is among the biggest box-office attractions in world rugby.
“It (World Cup leading try-scorer) is something that is in the back of my head, but getting the wins is all that matters,” he said.
“I would love to be top try-scorer. As long as we win all the matches, that is the end goal. I am buzzing with the result – we are building nice momentum going into the quarter-finals.
“I am definitely a quicker player now. I am a lot fitter as well, which means I can repeat these things.
“I know Gats (Wales head coach Warren Gatland) has spoken about my training schedule.
“I haven’t missed training for a couple of months now, which is great. I am buzzing with the way I am playing at the minute – I am trying to do everything I can to help the team.”
Wales assistant coach and attack specialist Alex King fully acknowledges Rees-Zammit’s value ahead of a fourth successive World Cup quarter-final appearance.
Rees-Zammit was the only Wales back to start all four group games and he scored tries in three of those against Fiji, Portugal and Georgia.
King said: “We are lucky to have a player like Louis. It’s great for rugby to have these kind of stars with finishing power like that.
“He is a fantastic athlete, he is quick and his game has really come on in the last 12 months.
“It’s his mindset, his attitude, his professionalism, everything you need to be a top player.
“He is still very young, he has got 30-odd caps for Wales, he has been on a British and Irish Lions tour and he just wants to get better and better.
“We want to get the ball to Louis, but it is not as simple as just giving him the ball. Defences are very good.
“His attitude has been first class. He wants to get better and better every day he turns up to work. He was great (against Georgia) and I am looking forward to Marseille next week.”