Explain is a word. It consists of two syllables, ex and plain. The is a one-syllable word. Difference is a word. It consists of three syllables, dif, fer, and ence. Between is a two-syllable word, be and tween. With and an are both one-syllable words. Example is a three-syllable word, ex, am, ple. There are single-syllable words and multiple-syllable words. I hope that explains the difference, using words from your own question.
I agree with the above answers. I wanted to add that there are two ways we teach elementary school students to find the syllables in a word. One way is to clap out the syllables. As you say a word like "difference" you clap each time your air becomes blocked. With the syllable "dif-" your tongue is touching the roof of your mouth, blocking your air flow. With the syllable "fer", your teeth touch your bottom lip, again blocking your air. And lastly "ence" your tongue touches the back of your teeth, blocking your flow of air. This makes three syllables.
The second way, is to hold your hand under your bottom jaw. As you say a word, count the number of times your jaw pushes your hand down. This will be the number of syllables in the word.
every word is made up of one or more syllables, but a syllable is a part of a word.