If you don't already understand IP Routing, then the results from traceroute will not tell you anything. The route between two nodes over the wider Internet can change from second to second. And the route in one direction is not the same as the return route. And that's not even accounting for the fact that the specific case you mention uses a CDN, meaning that not only can the route change, but the actual machines you are talking to can be different.
Having said that, there is no guarantee that the route you get from traceroute is the same as your application is using. This can be for several reasons (probably more than a dozen, if you count obscure cases), including:
an ISP in the path that purposely routes traceroute packets differently to hide their topology
the topology changes in some way between the traceroute and the TCP SYN
there is some form of load balancer or CDN that purposely redirects some traffic
Those are the most likely ones that I can explain without delving deeper into how the net works.
And, by the way, your comment "different operating systems may use different packet types" is incorrect. Every system connected to The Internet uses all those packet types, you can't operate on the net without them.