I'm not finding a reasonable graphic representation of a modern sailboat rig, but it sounds like you may be looking for the basics, rather than an in-depth discussion of every reasonable variant of modern sailboat rigs.

Usually when people ask about a sailboat's rigging they are referring to the wire ropes which are used to hold the mast in place and transfer the forces developed by the sails into the hull. These wire ropes are the standing rigging, because they are permanently in place and don't move. Another element of rigging is the running rigging which is used to hoist, trim, and adjust the sails and spars while sailing, usually of non-wire rope these days. (Incidentally, a sailboat's "rig" is the arrangement of sails on the boat, while the "rigging" is the actual wire ropes; that's a minor jargon use which can cause confusion.)

The wire ropes used to keep the mast upright and in column, and to transfer the loads to the hull, generally work to prevent movement fore-and-aft or side-to-side. Fore-and-aft wire ropes are called stays, and side-to-side wire ropes are called shrouds. Spars include all rigid struts used in the rigging, including the jumper struts used to improve the angle of the shrouds which are called spreaders in North America but may be called crosstrees in Europe.

Stays are very simply named on modern boats. The aft-most stay is the backstay. The fore-most stay is usually the jib stay or the fore-stay. If there is an inner stay it's usually called the inner stay, sometimes the staysail stay.There are a few more esoteric names for particular uses, for example a running stay on a rendering bowsprit may have a special name, but I'm just going to cover the most common standing rigging.

The standard shrouds are the cap shroud, top shroud, or masthead shroud, which goes to the top of the mast, and the lower shrouds or lowers which are often paired - a fore and an aft lower on each side of the mast - and lead from the base of lowest spreader to the deck. Some vessels will include intermediate shrouds, such as almost all boats with more than one pair of spreaders. More complex rigs often ignore these traditional names and describe the rigging as panes with an alphanumeric system (D1, &c.)

Any spar used to spread sail may involve the use of standing rigging to spread the loads into the hull. So, a bowsprit, which is the stick at the bow of the boat used to push a sail forward of the hull, may have stays (forestay and bobstay) and shrouds, and spreaders (often called whiskers, but the bobstay may also have a martingale sometimes called a dolphin striker, or a seal striker at Brion Toss's shop.) But any spar can also be set up to work without any standing rigging, such as the masts of the original Freedom 40 by Freedom Yachts and the bowsprits of many racing craft.

Many rigs, such as those used on catamarans, have additional specialized rigging. These are just the most common standing rigging items.

Rigging can be made of things other than wire rope, too. Racing boats, especially, may try uncommon things to reduce weight aloft such as using rod rigging (which is a wire rope with only one strand) or high modulus ropes and dead-eyes (which is very similar to what was used on traditional tall ships from the golden age of sail.)