By Balazs Koranyi and Francesco Canepa

FRANKFURT (Reuters) -A big interest rate cut from the U.S. Federal Reserve on Wednesday raised bets on further policy easing at the European Central Bank in October but this is still not the most likely outcome given different economic realities.

The ECB has already cut interest rates in June and earlier this month, and many at the bank have hinted at steady, quarterly rate cuts ahead to make sure inflation is defeated on a durable basis.

While the Fed's apparent rush lends some support to arguments that the ECB is falling behind the curve given rising recession risks, the fundamental economics have not changed overnight, so policy hawks on the Governing Council can make an argument for waiting until December.

"That the ECB needs to cut in October because of what the Fed did is a ridiculous argument that wouldn't fly on the Governing Council," Dirk Schumacher, an economist at Natixis, said.

"The only way to argue that is to say that it (the Fed cut) will change euro zone data and that may be the case but we haven't seen it yet."

This is also reflected in market pricing, which now sees a 35% chance of a 25 basis point deposit rate cut in October, up from 30% a day ago, a small but still notable shift that leaves December as the most likely date for an ECB move.

The ECB is likely to take it slower because it has a lot less to do.

It has five, maybe six 25-basis-point cuts until it reaches a "neutral" interest rate level at around 2.0% or 2.25%, according to various estimates that include the ECB's own.

The Fed meanwhile has probably eight such reductions until then, so the world's top two central banks might still reach their end point of policy easing at the same time.

Then there are the fundamentals.

Euro zone inflation, now at 2.2%, could tick up towards 2.5% by the end of the year and will likely come down only slowly to 2% by the final weeks of 2025 as entrenched wage pressures push up services costs.

This is why conservative policymakers, or hawks in market jargon, have cautioned against moving too fast.

Slovakia's Peter Kazimir has already pushed back on October while influential rate setters Isabel Schnabel and Klaas Knot have both in the past made the arguments that quarterly moves to coincide with fresh projections made sense.

"Inflation is currently not where we want it to be," Bundesbank chief Joachim Nagel said on Wednesday.

Conservatives, who drove a record string of rate hikes in 2022 and 2023 are still likely to be in a majority and that is why markets are not repricing ECB moves after the Fed decision.