OK, now I'm on a real computer rather than on a dumbphone, trying to fat-finger detailed information. So, let's try:
In the cable TV business, there are splitters. They've got powdered-iron doughnuts with coils of wire around them inside, that sort of thing, and they send your channels all different ways. They also cut the strength, but nothing's free. You have one that's powered. Is it "bi-directional"? That's required, if you have your cable modem on one of the split outputs; internet data signal has to go both ways, after all.
Now, you Could put a second cable modem in the shop, with the following restrictions: you'd split the cable from the street, into two paths (see "splitter" above). One goes to your house and one goes to the shop. You'd get an additional internet bill, same as for a duplex residence where one cable goes into both homes or apartments. The other restriction is that, should you want to trade files or pictures or do backups, stream video from the house, etc, you would have a much harder time at it. (OK, those of you who know all of this stuff - I know what can be done with port forwarding, VNC, FTP... that's well beyond the scope of this help.) Therefore, we can concentrate on straight networking. First, some terms to know:
LAN - Local Area Network. Essentially, everything computer-wise, TV-wise, WiFi-wise, on your household's side of the cable modem.
WAN - Wide Area Network. The system that brings the internet to you; all of that stuff on phone poles, in the ground, the massive infrastructure that lets us chat like this.
Hub - This is your "splitter" in the context of network lines in a business, home, school, etc. The hub takes requests and forwards them to the router, which speaks with the cable modem. And so on. Information returning from the web are passed through that other stuff back to the hub, which sends it to the output lines connected to it. Your computer hears it, while the other devices couldn't give a shit until a data package with their name on it comes along.
Switch - Pretty similar to a hub except that it sends info to and fro, only between the parties for which it's intended. Not quite as much a "party line" as much as a locomotive turntable, in concept.
Access Point (AP) - a two-way radio that entertains connections from your play toys and work machines, without needing a run of network line between each or any of them, and the stuff that delivers internet into the home, etc. Also known as a Hot Spot, though some might posit that a hot spot refers to an AP open to all as opposed to a passworded system.
Ethernet - describes a particular type of flexible cable that has 8 conductors inside. Moreover, the industry refers to this as 4-pair (because, you know, twice 4 = 8). In order to reduce or eliminate electromagnetic interference, each of the 4 pairs of marked wires are twisted together as pairs, then, the whole mess is twisted together as a whole. One twist essentially nullifies noise picked up by the opposite twist just up or down stream. Yawn. Suffice it to know that, for all practical purposes in a home LAN, Ethernet and the abbreviations Cat5, Cat5e, & Cat6 may be considered interchangeable for these discussions.
RJ-45 - The type of plastic connector that facilitates joining Ethernet cable to a device that needs it to communicate. They look a whole like a fat, wide, telephone line male wall plug.
DHCP - Dynamic Host Configuration Protocol. Fancy talk for handing out name badges, or, phone numbers. Your cable modem has an identifying number similar to, say, 188.8.131.52 which is assigned by the cable company. This is called an IP address (for Internet Protocol). Such addresses are necessary for every internet site in the world, for the same reason your phone has its own unique number. Only one DHCP "server" can exist on your network, lest your hardware not know with which device to exchange information both in or out.
Client Device - Anything that you're going to hook up to your LAN. For these purposes, I will chiefly use the term as it pertains to WiFi-connected devices. You can, in fact, buy a "client device" as a WiFi receiver, then, hook that into a computer or instrument that only has a Cat-5 connection available. A client device makes a non-Wifi thing into a WiFi-enabled thing.
Router - Combines the function of a network hub and the function of an access point but with additional intelligence. For starters, it takes information from your cable modem and sort of changes it's address so that stuff on your side of it is somewhat protected. Referred to as Network Address Translation, everyone in the world will see your house IP address as shown above but they can't see you, specifically; your product box probably boasted about a NAT Firewall. You can see out but they can't see in (without you permitting it). Within your LAN, it may look like 10.1.1.69 or some other scheme - but not like the address the cable company assigned you. The DHCP server in your router will give each of your toys their own specific number address within YOUR private system (LAN).
WiFi - "Wireless Fidelity" as it was originally called; the wireless, range extending ability by which an access point works. There are evolving standards, whereupon the newer stuff is generally compatible with the older stuff, at the older stuff's range and/or speed limitations.
Network Bridge - A wireless way to get your LAN to serve a place where running Ethernet is a pain in the ass. Strictly speaking, it describes the receive end in the sense that a Client Device, connected to your router, constitutes a "bridge"; In our context, the network bridge will consist of two separate and dedicated wireless appliances that work together, to bridge that gap (due to it being a pain in the ass to run 4-pair wire...).
OK, so, that's the meat and potatoes of it. If you choose to use adapters to get your CAT5-laden signals across the yard, all you need to do is to run a Cat5 line from the place where your RG-11 meets up with that on the house end, over to your existing 4-port router that you've mentioned having at the house already. On the shop side and once RJ-11 signals are converted back to Cat5 wire, you will need another switch or hub to plug in any wired components in that building - if there is to be more than one gizmo out there. If you want WiFi alone out there, you need only find an access point that you can serve electricity and the Cat5 wire you just extended there by whatever means.
If you want a place to plug in Cat5 lines out in the shed and also have Wifi, you can either look for an access point that allows this - or, you can take a full-on router (or an older one not used any longer) and set it up do do this. The main thing is that you disable DHCP in the soon-to-be 4-port Wifi distribution point. Plug your Cat5 line (from the cable adapted from prior Cat5 at the house) into one of the four LAN ports, NOT into the WAN port that in an earlier life used to take signal from the cable modem. Yeah, you'll actually only have three plug-ins, but if you're running stuff out there that requires wired hook-up, you can add a switch to one of the 3 remaining holes and get back 4, or 8, or 32, or any number of ports depending upon how much you want to spend. Choose something clearly marketed as a Switch, all else being roughly equal.
The other plan for spanning the 200 ft to your shop will still require a Cat-5 line from your home router to a place with an unobstructed path ("line of sight") from that point to a convenient mount point at the shop end. You will still need your choice of an AP or a re-purposed router (new or used). The chief difference is that you'll put the money that you were going to throw at coax-to-RJ45 plugs, into some good grade network bridge radios, such as I've mentioned in earlier posts.
If you like, I can scare up a block diagram that demonstrates the wired vs. bridged paradigms. Now go have a beer.