Is chaining two switches different than connecting both switches directly to the router?

Amongst other things (like what haroldmoma mentioned), another to consider is that if you chain the switches together and the first one dies, the second one will also stop working (everyone is offline). If you attach them both to the router, then one failing won't affect the other (only half the office is offline).

When you connect two switches together, you are extending your broadcast domain. The broadcast domain can impose a burden in fairly large networks. When you connect each switch independently to the router, there will be a broadcast domain for each switch, thus controlling the broadcast traffic passing through your network.

If you chain the switches the switch closest to the router will get more traffic than if you had put them parallel (where it will all go through the router) depending on your usage (heavy internet accesses needed vs heavy access to own fileserver) you can weigh one off to the other.

It makes the switch closest to the router a single point of failure (as mentioned by techie007).