I am currently studying for MY MTA 98-366. What is the different between the standard firewall that comes with your wireless router your isp provides compared to a cisco firewall..
Intended use and everything that goes with it.
Your home router has a basic packet filter slapped on for some basic, added protection. Some of the more advanced ones will even have stateful inspection. I'm sure that NGFW features will make it to the consumer market in due time. The main takeaways are that the technology is very far behind enterprise stuff and it's really there as a marketing gimmick for clueless home users who are scared of getting hacked.
An enterprise firewall is more of a security appliance that provides a suite of security services needed for business use. These days everything can do packet filtering and even routing, but a firewall is expected to have VPN functionality, clustering/failover, and alerting/reporting, at the minimum. The new thing is NGFW which includes application level filtering, an integrated IPS and centralized management.
It also needs to be able to handle tens of thousands of concurrent connections and it will have the hardware needed to do that - your typical D-link router is going to crap out if it tries to pass normal traffic for a thousand devices, nevermind encrypted VPN traffic.
Really, I think the better question would be the difference between modern enterprise routers, switches, and firewalls. The difference between consumer grade and enterprise gear is like comparing a bicycle with a racecar.
It's still a router with a switch correct?
Router, yes, switch - not necessarily. A lot of firewalls do have switchports, but some don't. Some will have layer 3 interfaces but allow for virtual switching through software. It's not a defining feature. Even if you do have swichports, you'll still need a switch unless you've only got a small handful of physical devices.
Why is it advertised as a just a firewall?
As I mentioned before, if you're shopping for a firewall then you're looking for a particular set of features and capabilities beyond just basic packet filtering. If someone advertises a firewall then I know what the basic feature set is going to be.
Do all wireless routers have firewalls?
Pretty much all modern consumer grade home routers have some kind of firewall functionality included, these days.