I did a 104-mile ride last summer with 6,200' of climbing. I would consider that to be fairly hilly, but certainly not mountainous by any means. There were long drags, plenty of little, almost constant, rollers and a few long, steep hills on that route. It was a mix of N.E. Ohio hill types on or near the glacial terminal moraine.
The spacing, steepness and length of the climbs have as much to do with whether a given rider considers a particular ride to be 'hilly'. A century with one good 5000' mountain to get over in the middle of the ride may or may not be considered hilly if the rest of the ride is pancake flat. A century of constant steep, but short, climbs that added up to 5000' would be considered hilly by most riders.
I agree with Weatherby regarding climbs and gearing. It should be added that different types of riders prefer a certain type or types of climbing. Some riders do not consider the long, shallow 'grinds' to be climbs at all while that same gradient might really put the hurt on the next guy in the pace line. A steep, punchy climb may suit one fellow and his riding partner might struggle on that same wall.
It's all...relative, OP, like you said in your first sentence.
Brian Toone, one of STRAVA's climbing statistic record holders, would probably call a 10,000' century 'flattish' while my legs would definitely term that a very hilly/climbing ride.