On Demand
Reserved Instances
Serverless
BYOL (Bring Your Own License) - only for Oracle DB and both for On Demand or Reserved Instances
On Demand instances can be launched at any time within minutes.
Price depends on instance type. In case of Multi AZ deployment you will incur in additional costs (usually double).
With Serverless there are no instances to manage so pricing is measured in ACUs ( Aurora Capacity Units: 2GB of memory) per hour.
Reserved instances allow you to purchase a discount up to 75% for an instance type for a set period of time (from 1 to 3 year) and depending on payment method ( all upfront, partial-upfront, no-upfront ) you can get further reductions.
Storage and I/O pricing varies across different DB Engines and it has to be considered too.
Aurora uses a shared cluster storage architecture while all other DB types use EBS (Elastic Block Store)
You can check my previous post about EBS to find out different storage options and its pricing.
In case of Aurora and shared cluster storage architecture, you can't configure any storage options because it will be managed for you automatically, and that is why the pricing metric is in GB months + number of I/Os processed ( billed per million requests)