What's included in a Colosseum ticket
There is no Colosseum-only ticket. Every official ticket bundles three sites, and the time you get for two of them depends on which ticket you buy.

Photo: BeBo86, CC BY-SA 3.0, via Wikimedia Commons.
The three-site bundle
Every ticket type on this site covers the Colosseum, the Roman Forum and Palatine Hill together. You cannot buy entry to just the Colosseum. The Forum and Palatine sit right next to the Colosseum and share the same archaeological park, which is why the ticketing authority sells them as one admission.
The validity window that actually differs
What changes between ticket types is not whether the Forum and Palatine are included, but how long you have to use that part of the ticket. 8 of the 10 ticket types give you 24 hours to visit the Forum and Palatine after entering the Colosseum. Arena Floor and Underground tickets, 2 of the 10, extend that to 48 hours, so you can split your visit across two days without paying for a second ticket.
See the arena floor ticket for the full 48-hour breakdown, or go back to all ticket types.