Just wondering if a pad is just like any synth but they just extended the envelope and gave it a bunch of reverb and echo?
Reverb and echo have nothing to do with it. Many old synths have no reverb or echo effects of any kind, yet they're full of "pad" sounds. A pad is a steady, long sustained sound with a non-sharp attack that's used for filling the soundscape. A Hammond organ can be used as a pad if the attack is softened and the sound is let ring steadily.
In synth jargon, "leads" and "pads" are broad categories of settings that make the sound either more bright/foreground or more dark/atmospheric respectively.
A lead synth is normally used for melody lines with more high-end and volume, and pads are used for background swells (slow attack) often with chord/reverb patches applied.
So yes, your impression is generally correct.
All you can really say is that a lead sound is suitable for taking the melody, a pad is a sustained background sound.
You'll find 'string pads' with slow attack and release. Note that this isn't what real string instruments actually do most of the time. They can play with considerable attack and handle nimble, fast melodies.
Leads and pads can be converted between each other by changing the attack and decay/release.
A lead generally has a very short attack (meaning that when a key is pressed, you hear the note almost instantly) and the release (how long it takes for the sound to die out when you stop pressing the button) is often pretty short too.
A pad typically has a longer attack and a much longer release, but that isn't the only way to make a pad sound. Usage of delay and reverb can indeed draw out the sound of a pad, although personally I don't like the way it sounds. Other ways of lengthening out a pad note is to continually play more of the same note.
Pads don't have to have long releases. Practically, whenever I have a pad in my songs, it is maintaining a note or chord for a bar or two before changing to a different note/chord. Typically I don't want the tone to take forever to die out, nor do I want the note change to be instantaneous. I just want to blend it with the next note coming, so I use a relatively short release so that the note change isn't either intrusive or lost.