I also depends very much on the style of climbing you’re doing: top-rope, sport lead, traditional lead (trad), or ice climbing. Also, whether you are climbing single pitch routes or multiple pitch routes, and what kind of training you have for any or all of the above.
You should not be climbing outdoors without taking a course. Leading outdoors (sport or trad) you’ll especially want a course that covers everything from properly using your gear, permanent fixed gear you may expect to find on the rock face, and basic self-rescue. For top-roping, you should also take a course in how to properly (and safely) set-up top-rope anchors, rapelling, and related safety procedures.
When I first started climbing, there were two local fatalities. One was a guy who was setting up top-rope anchors without leashing himself to anything before approaching the edge. He just slipped over the edge when he was looking over to see his friends below. The other was a guy who lost control of a rappel - a prusik knot (requiring not even $1 worth of cord) would have prevented his fall. Falls due to equipment failure are rare. Most are preventable screw-ups.
General comparative risk:
Top-roping: If proper, “bomb proof” and redundant top-rope anchors are set up, the danger is pretty much identical to top-roping indoors. The dangers that differ from the gym are environmental: rock fall, sun stroke or dehydration, sudden weather changes, and angry wildlife (e.g. rattle snakes). Top-rope routes are also limited in height by the length of your rope, and few top-rope routes go higher than 40-60 feet.
Sport leading: for the most part, as dangerous as sport leading indoors, except you also need to know how to recognize deteriorated fixed gear, and how to clean your gear from the cliff-face (cleaning gear is probably the riskiest part, IMHO). In addition to the multiple day course we took, my fiancee and I have taking refresher courses prior to each major expedition to make sure we haven’t developed any bad habits. Environmental risks are the same as above.
Trad climbing: (which you can’t do indoors), is certainly not for the risk-averse, as it has the most potential for both human error and bad luck. I have been rock climbing, indoors and outdoors for about 20 years now. I don’t trad because the risk outweighs the fun for me.
Generally, IME, most common serious injuries are rappelling injuries, falls sustained while setting up anchors, or easily preventable mistakes that occur while you’re actually in the least peril but most easily distracted by the mundane. For example, with both feet firmly planted on the ground, you unbuckle part of your harness to pee, then forget to do it back up again, resulting in an injury later.
As in Sage Rats link, a large number of injuries outdoors are serious but survivable. E.g./ you fall, your rope catches you, but the during the shock-absorbing rope stretch, you catch your ankle and break it. You should note that Sage Rat’s link is also about Yosemite - BIG WALLS - that are mostly multi-pitch trad climbs that can takes days to complete, so you will be sleeping overnight suspended from the cliff face.
Those stats reflect the injuries and fatalities for Yosemite, not outdoor climbing in general. For example other major climbing areas such as Rumney and Red River Gorge will have very different stats, since the nature of the climbing at those areas is radically different.
I have nothing to say about ice climbing because I’ve never done it. I don’t like the cold and I don’t like the unpredictability of ice.