A chain is a sequence of moves where a portion of one move's animation is "canceled," and the following move executes immediately. Chain combos are generally easy to perform and don't require very precise timing. Some games have universal chain combo systems -- such as the "magic series" in many Capcom Vs. games -- and many games have character-specific "target combos" that chain specific moves together, such as Ken's
MP -> HP.
A link is a sequence of two moves that occur one after the other, without any cancellation of animation frames. For a link to work, the first move has to leave your character with enough frame advantage to execute the second move before the opponent is allowed to block or otherwise avoid the attack.
Because no animation cancelling occurs during a link, this means that if the second move's button input is performed too early, nothing will happen (because the character will still be in the recovery animation from the first move) and if the input is performed too late, the second move may be blocked (because the opponent will have recovered from the previous move in time to block). This makes links generally harder to perform than chains, sometimes much harder: "one-frame links," for example, must be performed with frame-perfect timing.
Your particular example is a little bit more complicated because in many Street Fighter games, Light Punch and Light Kick can often be chained into themselves -- and each other -- indefinitely. Moves that are chained into in this way, however, generally can't be canceled into special moves. In your example combo, you could chain the first two LPs together, but the final one must be linked into, so that it can be canceled into the SRK. If you don't, the SRK won't cancel the last punch, so it will come out late enough to be blocked. What this means is that you need to wait for the second punch to finish, then precisely time the third punch's input so that it comes out late enough that it doesn't cancel the preceding move, but early enough that it still combos properly.
In combo notation, that particular combo would look like
LP xx LP, LP xx HP SRK.