I'll let majority decide on that but imo earmarked funds funneled into savings for a specific purpose (ie. holidays, vacations, insurance, maintenance, etc) is different than an EF.
Like my savings to replace my tv, improve our bonus room and upgrade my old furnace and central air are not my EF savings. Even though the furnace dying would be an emergency, I'm saving now to avoid it being a true emergency and am not using EF money toward it. My EF is more for survival planning (ie. ours saved our butts when Gabe was unemployed) than repairs or replacements even if they come as a surprise.
But I realize this is going to be different for everyone depending on where they are financially or their own perspective. A car needing repair can be an emergency for someone and not for someone else. However, I think repairs should be budgeted in and are separate from an EF.
But for some folks, I think building ANY savings is beneficial, so wouldn't want to discourage anyone by making it more complicated than it needs to be.
ETA, to me EF and sinking fund should be separate, but if you're disciplined, you could simply categorize and create something in I don't know Quicken or whatever that allocates amounts vs. having actual separate accounts.
So my opinion is separate. We can have a sinking fund challenge, too. Get people to start budgeting in expenses that are likely or definitely going to happen. And leave an EF the way it's designed to be.