There's another difference.
For the type shown in the video of taegeuk4 - which we would refer to as a fingertip thrust (we don't have spearhand as a regular use term) - the attacking hand is vertical.
The orientation of the hand depends on the target (more below).
The secondary hand, the one that finishes under the elbow, palm down, lands there having travelled in an arc motion - kind of performing a high downward palm block (say to an incoming punch) - then the attack goes over the top. These aren't generally visually discernible as separate moves.
The 'advanced' bit, that could still follow - so sweepy block to a punch combined with thrust over it, grabbing the hand you've blocked to pull into another move...
At least, that's how we do it.
The type shown in T4 - target would be mid section, so solar plexus area or thereabouts. Always vertical, palm to the side.
A high section (eyes, septum area, throat) would generally be a "flat fingertip" which is horizontal hand, palm down.
Low section (stomach, groin) would be "upset", so horizontal again, palm up.
That's how I take it too.