An Extreme has more features, and at least in older iterations was more powerful. Big extras were the ability to attach a USB hard drive to the Extreme, but the Express, aside from portability, has that cool jack for attaching audio devices that allows you to beam music to it (especially cool with Airfoil; look it up). You cannot attach USB drives to an Express; its USB is for printers.
Both can let you port forward, but only one should do that at a time.
It's easier to use a Mac with either, mainly because Apple, unlike most every other manufacturer, uses it's own application, Airport Utility, rather than a web browser
. I'd say that it's marginally easier to use an all-Apple network, but not in a big way. Hassles often occur anyway, and a likely problem area is the connection with your ISP, which isn't Apple, and whatever gateway/cable modem they use. Apple uses somewhat different nomenclature, and firewall configurations, although they all are the same behind the hood. But, although expensive, the Apple stuff is good quality. If you are gonna use a drive attached to an Extreme, it's definitely better because more other routers that have that feature require a different file format for the disk, which is a pain if you use Macs. With the Extreme you can just attach it to your Mac with USB if you have to and not worry 'bout mounting issues, etc.
I prefer Extreme plus drive rather than TC. With a TC, if the drive fails you've got a router with a paperweight. YMMV.
Time Machine is a bit of software. It doesn't depend on whether you have a certain kind of router, but Time CAPSULE is designed to use it, and I think it's the only officially supported network storage that Time Machine can use. But I think people have used other network storage with either Airport Extremes, but it's less reliable. Again, YMMV>
TM backups will grow and grow until they run out of the space you assign them, whether it's on an internal, external or TC. So they could be of different sizes, and even have other stuff already on them. TM will then begin to delete ONLY the oldest VERSIONS of files it has backed up. Not the other non TM files, and not the only copy of any file. It's generally not a bad idea to partition the drive you have for backups just to preserve some more space though, since you may not know how big that TM backup has gotten, and you wanna be sure you have enough space to store all the Bullwinkle videos you're collecting.
Again, Time MACHINE isn't a machine, it's the software. The Time CAPSULE is a machine, a hard drive and router combo. Now that I write this, I feel your pain.... A Time Machine backup is a group of files that the TM software wrote on a Capsule or other hard drive you designate for the Machine, er software, to backup to. Sheesh.
Apple TV is yet another uber-Apple product that basically is a front end for the iTunes Store...just kidding, barely. It's basically the only way to get streamed video from a Mac to your HDTV wirelessly; that's AirPlay video. You can audio to Apple TV, the Express, iDevices and some third party products, but that's AUDIO. Some Mac software will also stream video to iDevices as well. So yeah, it's optimized for AirPlay. But if you don't mind connecting with wires, it's a meh. There are many ways to connect an HDTV with a Mac that don't involve your network. And AirPlay can work with a wifi network that is created with a non-Apple router. Time Machine is backup software; it basically has nothing to do with AirPlay.
PCs and any other device that uses wifi or ethernet should work fine with an Express or Extreme. You may see some devices that are easier to configure because they use UPnP (plug and play), which Apple isn't really into, but it's usually a matter of opening an appropriate port, making sure you don't have a double NAT (which means two routers trying to direct traffic at the same time), and generally following instructions. I've had PS3s, Directvs, TiVos, PCs, Linux boxes, printers of all sorts, and even the hardest of the hard, security system DVRs, running on a network accessible through the internet and uverse and ATT DSL and cable with success. Not saying there aren't hiccups, but it's doable. And kinda fun in a ham/hacker/techie way. Check out smallnetbuilder.com; good source of general networking know-how not limited to Apple.
Have fun! Judging by your intelligent questions, you'll get it all sorted.
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You can use the storage of TC any way you want. Time machine is designed only for TC.
I think you can partition the drive in the TC, but I don't own one. Just google it.
TC and APExtreme are faster than APExpress and have a better range.
I don't think you meant this, but Time Machine is designed to be used with more than the Time Capsule; it will work with virtually any external USB or Thunderbolt or Firewire drive, for example.
And although you can't partition the drive in the TC, if you use an Extreme with an attached USB drive you can, of course, format that by just connecting it to a computer via USB. Handy.
