Let's see if we can illustrate this. First thing, lets discard the notion that 3d6 and 1d18 are potentially equivalent. We know this cannot be the case as 3d6 cannot roll less than 3. So let's compare to something slightly more comparable. The result set of 3d6 has the same numbers as the roll of 1d16 + 2.
Rolling a 1d16+2, we get numbers from 3 to 18 with equal probability. The likelihood of rolling a 3 is the same as rolling an 18. (1/16th). (the probability of rolling a single number on a die is 1 over the number of sides).
Now. What's the probability of rolling 3 ones on 3d6? First thing we need is to know the number of possible result sets of rolling 3 d6s. This is called the number of permutations. To get this we multiply the number of results from each die together.
6*6*6 = 216
We will use this number as the divisor when calculating probabilities (just like we use 16 for 1d16+2). Now we need to know the number of possible permutations total 3.
111 1 + 2
That's it. This gives us a probability of 1/216 for a result of 3. That's very different from 1d16+2. The probability of all 6s is the same (666).
Now. What's the probability of the next result? rolling a total of 4? Well to roll 4 we need a 2 on one of the dice and ones on the others.
112 2 + 2
This gives us 3 possible results in 216 possibilities. Thus a 1/72 chance. Again vs a 1/16 chance for 1d16+2. This is mirrored with the chances of rolling 17. (665, 656, 566)
I'll go one more. The sum of 5. the possible results:
113 3 + 2
Here we see 6 possible results. That means the odds of getting a sum of 5 are 1/36 again vs a 1/16 chance for the 1d16+2. This is mirrored by a result of 16.
As you approach the middle you have a multitude of possibilities. Let's look at a result of 10 (just under the average of 10.5 for the 3 results).
136 226 316 415 514 613 8 + 2
145 235 325 424 523 622
154 244 334 433 532 631
163 253 343 442 541
262 352 451
That's 18/216 = 1/12 compared to 1/16. (This is mirrored for the result of 11).
The mirroring of results, combined with the changing probabilities illustrates the bell curve. Whereas the constant probability of a single die is a single horizontal line.