The pool table, its light, and the surround is where all the action happens.
Pool & Billiard tables are sized as a 2x by 1x rectangle. Pool (pocket billiard) tables have pockets in each corner and half-way along the sides. Table sizes are characterized by the table length in feet: Usual table sized are 7, 8, and 9 foot in the US.
A pool table has sturdy legs which support a subtantial frame.
The frame is substantial because it has to support slate (aka rock) top that is the playing surface. Usual slate thicknesses are from 3/4 to 1-1/4 inch thick. Larger tables, carom tables, and higher quality tables can have even thicker slates -- IIRC the thickest slate used on some tables is 2" thick -- that is a lot of rock!
Smaller tables (such as bar tables) often have one piece slates, while larger 8 and 9 foot (and the larger 10 and 12 foot) tables have 3-piece slate tops. This keeps the weight and size manageable. The slates are levelled up on top of the frame. Levellers on a frame can be simple wood wedges, hi-tech wedges with screw jacks to position them, or plain adjustable screws.
A Surround sits on top of the frame, and also the slates. The surround is the edge (apron) of the table, and also is part of the and upper top of the pool table, which provides a backing for the rails.
The Rails are rubber bumpers of a certain profile that line the edges of the table and the pockets. The rails provide the rebound effect that allows balls to bounce off the rails and continue rolling along the table. Higher quality tables have better quality rubber rails. Both the profile and the rubber quality can be higher. These rails reflect the balls more perfectly with lower speed loss. The difference between cheap rails, bar box rails, and tournament rails can be amazing. It can also be frustrating to deal with the difference in their performance!
The slates and the rails are covered by a fabric or cloth, also refered to as felt. There are various speeds of cloth, from slow to fast. Smaller tables are often covered with a slow fabric, and larger tables covered with a fast fabric. This has the advantage that a similar shot strength works for similar (diamond, not distance wise) shots on both tables. A fast fabric is really fast, the increased distance doesn't slow the balls down as much.
The fabric also has an effect of how the balls rebound from the rails, and affects bank angles as well. Dirty or old fabric has different (and sometimes opposite) effects than new or clean fabric. It all makes for an interesting game -- there is reason why people want to hit a few balls on a table before shooting a game -- they want to get dialed in to how that table rolls. How fast the fabric is, how the rails behave, and how open the pockets are.
A pool or pocket billiards table has ... you guessed it, pockets cut into the rail at each corner and halfway along the long sides. The pockets are edged with the same rubber and fabric as the rails are. Pocket sizes can vary considerably between smaller pro cut pockets (barely 2 balls wide) and larger sloppy pockets which can fit 2 balls with room to spare. The pockets also have shelves, the amount of slate which continues beyond the edge of the rail to where the balls can drop into the actual pocket. A larger shelf means that there is more table from the edge of the rail to the start of the drop in the pocket. The entrance angles cut into the rails to the pockets also vary from table to table.
All these effects -- pocket size, shelf width, and pocket angles have a large effect on the pocket-ability of balls on a table. Bar Boxes have small shelves, large pockets, and more acute entrance angles on the side pockets compared to regulation tables. This means that the corner pockets in bar boxes often let almost any shot drop! It also means that the side pockets on bar tables are less forgiving than side pockets on a regulation table. How so? The entrance angle into the pocket is tighter, meaning balls can be pocketed into the side pockets from a smaller region of the table. The entrace angles really make things worse: instead of balls dropping into side pockets they often bounce out directly from the face of pockets! Tournament cut pockets on regulation tables are even narrower than pro-cut pockets. Basically the rails are a bit longer than normal to make the pocket entrance smaller. These pockets demand an even higher level of accuracy to pocket balls without the balls rattling in the pocket.
Some tables have Drop Pockets where the balls just drop into a plastic or leather mesh container after rolling off the shelf into the abyss. The better tables have large drop pockets on all 6 pockets, which allow for almost 15 balls in each pocket. Lesser tables often skimp on side pockets -- some side pockets only take 6 balls before filling up. Other tables have Ball Return Systems, which return the balls to a collection box at the foot of the table. Most bar boxes have some feature to sort the cue ball from the object balls and direct the cue ball to the head end of the table. This sorter used to be size based, but on most modern tables it works with a magnet which attracts the steel layer in the cue ball. Some tables used computer-driven sorters, which allow any all-white cue ball to be used in the table, so the cue ball doesn't become trapped in the rack.
It seems simple -- a longer table is harder to shoot on because there is more distance between the balls and the pockets. It's actually more complex than that ... because the balls and pockets don't change in size with the tables!
Playing on a 7' bar box is a different game than playing on a 9' regulation table:
Don't get me wrong -- a talented player can play well on both tables. The base game is the same -- but the techniques and shots and tradeoffs change considerably. There is a similar type of difference between playing steel-tip and soft-tip darts. The board looks the same, but the trade-offs in the game change the way it is played considerably.