We went through this progression, and I agree 💯 with Jay and Moshe.
What are the business goals/requirements? Is it uptime or is it continuity? Both are tied together and both influence each other. Costs scale though as you add 9's to that availability and it usually is a combination of DR and HA.
Availability comes down to what Moshe said. Good CD and reliable deployments with blue/green or progressive deploys helps a ton here. You are bound by the uptime of your infra as well. If you're in AWS, you can only guarantee as much uptime as the combined possible downtime of the services you are using. If you're using s3 and it has an SLA per region of 99.9%, that's the best you can guarantee for your own stuff. For most people this is good enough.
If you have hot/cold (IaC using Terraform, standing up a new cluster from scratch in a disaster), you are going to consider RTO and RPO. How long does it take to recover and how much data did you lose? For a bit more infra costs and very little engineering overhead you can setup a Warm/Standby. All the infra is there but scaled to zero. Replication across regions. This will get you 30minutes or so of recover time, depending on how long it takes to make things hot.
Active/Passive was the next thing we looked at. Again you can do this without any engineering work. Your applications do not need to be built to support multiregion. There is more cost because you're paying for compute that is sitting idle. But with this you can use AWS global services to automatically switch between regions. This will get you more availability but at a higher cost.
Then you get to Active/Active. You usually have to do this in 3 regions and the apps your serving have to work across regions. You'll need to geolocate, possibly shard your database across location, etc... Cost scales up quite a bit in terms of infra and in terms of engineering efforts.
The long and short of it is, each 9 of availability you add with a combination of reliable deployments, failover/DR, and adding in multiple regions will increase costs, sometimes exponentially.