Does climbing hard outside mean you'll climb harder inside?

It seems like the consensus that outdoor bouldering is harder than indoor bouldering, but is it just because people usually transition from indoors to outdoors and are not used to the style/discipline? Or is it actually harder in terms of grades? Would somebody who started out climbing outdoors have trouble climbing indoors because they're not used to it?

Gym grades are soft to give beginners a more satisfying experience by having them progress through the grades a lot faster than outdoors. 

The only thing someone that went from outside bouldering to indoor bouldering would struggle with is parcour-style boudering.

Generelly the outdoor boulderer will be a more rounded and skillful climber (pad-placement, knowing when/how to fall, routefinding, being able to utilize smaller footholds). A lot of these skills aren‘t really useful in an indoor-environment and someone that only climbs indoors would probably climb harder (indoors) compared to the outdoor-boulderer because he doesn‘t need to focus on these aspects.

Depends. The indoor climbers have trouble adjusting to outdoors for one set of reasons. (No bright-colored footholds, scary landings, etc)

But the comp-style boulders that many gyms now set can also be challenging to someone who primarily climbs outside, because the moves are not something they encounter outside. 

I keep hearing about how these competition/parkour type of problems are only in the gym which is simply not true. Every bouldering area has its crazy eliminates that some regular has figured out in order to stump the bruhs or the folks who never try anything unless its in a guide with a hard # next to it.

Depends on your local bouldering. After bouldering outside instead of going to the gym for a few months during covid, I went back and was surprised at how much burlier gym climbing was than the granite areas of the Northeast (at the same grade). I'd gotten a lot better at crimping credit cards, weighting bad smears, and finding small rock features I could use to my advantage, but none of those help in the gym. 

On the other hand I suspect that if you boulder in LRC or Red Rock (or most sandstone areas?) you wouldn't have this experience.

Anyways, after two months of indoor bouldering afterwards, I got my indoor max back to my outdoor max (and my pre-pandemic indoor max) so apparently the necessary strength comes back quickly.

Nuances of style aside I’ve found commercial gym grades to be roughly 2 V grades soft if that gives you an idea. Ymmv. 

Have any of y'all tried doing actual parkour to get better at parkour-style boulders? No gym needed.

I find it difficult to transition back into the gym after a full season focusing on rock. I think it's primarily due to the volume of climbing I do in the gym in a much shorter period of time. Also the indoor problems are more consistent in difficulty throughout the entire boulder, so that requires a different approach and type of fitness. Skin is also an issue; hard granite climbing skin can make plastic holds feel heinous.

All in all I do find that once I adjust the skills I've honed outdoors do transfer to success in the gym, but my gym strength doesn't typically translate to rock unless it is a very specific type of problem (pulling on good holds/raw power).

Also, for the record, I can do precisely zero parkour type boulders.

I usually find myself bouldering better indoors after spending time bouldering outdoors. Outdoors bouldering tends to require better footwork and more body tension, and that’s helped my indoors bouldering. When the gyms were closed in early 2020, I exclusively bouldered outdoors doing a bunch of eliminates at the one rock available to me (Rat Rock in NYC) and when I went back to the gym in late 2020 I had gone up 1-2 V grades.

For lead climbing, I find indoors surprisingly hard compared to outdoors. It’s just so relentlessly pumpy, even though all the holds are jugs. The areas I climb at (Clear Creek, Boulder Canyon) are often less than vertical for most of the route with maybe 1 or 2 cruxes getting over a bulge or roof. So a 5.11 might be mostly 5.8-5.10 climbing with a V0-2 boulder problem crux, and often a great rest before the crux starts. If I dial in the crux then sending isn’t too hard. But in the gym, 5.11 is just relentless jug hauling on a 45 degree overhang. There’s no crux to dial in, it’s just pure endurance.

It really depends. I regularly onsight my outdoor bouldering redpoint grade at certain national chain gyms in Colorado and the East Coast (cough, cough, Earth Treks). However, at our local gym, over a 24 year period, I have NEVER managed to send my outdoor redpoint grade. I also rarely boulder, and even less so indoors.