Clones and echos are the same thing. Echo is just the new official word for it. Some echos or clones are just more alike than others.
Clone was in the past used for characters with very different base attributes.
For example, Link and Young Link, Pikachu and Pichu, Falcon and Ganondorf. The first two pairs are very different sizes and weights, Ganondorf is much slower (and somewhat heavier) than Falcon. Young Link's range is a lot less, Pichu has the self-damage mechanic. Aside from Young Link and Pichu whose hitboxes vary a lot from their source due to their size, all of the Melee clones have variations in damage/knockback/range/frame data on
almost every move.
Echoes by contrast have all been shown as identical or nearly so in size (Lucina being slightly shorter), weight, speed, and
most of their moves are completely identical (excluding adjustments for no tipper on Lucina). They can certainly have some differences and some unique moves, but Echoes are more similar to their source than any Melee clones (and clones after Melee tend to be more distinct than that).
So I'd say that an Echo probably has to have these elements:
Nearly identical size, weight and speed (so far we've only seen slight variation in size)
Most, but not all, moves and animations identical including damage/knockback/frame data (excluding taunts, idle animations, entrance and victory poses, etc.). Animations can vary more than hitbox placement... It's not important that Dark Samus doesn't hold her right arm during Charge Shot, for example, since it doesn't affect the move (I suppose it could affect her hurtbox during the move
slightly).