yup what you desrcibe origonally is econimy picking, it pupose is to create the minimum movement to play each note. so you can play faster. it is also good when are moving down three strings at a time.

alternate pickin is just always up down up down up, ( like the second example you wrote) regardless of note you are playing. i find this method easier as i dont have to think about it cos my hand just goes up and down up and down. i also find this helps to regulate rythm as my hand goes up and down at a constant rate and i just choose to hit or not to hit strings for rythm. although i dont always do this so it isnt like its necessary.

i would suggest you learn altenate picking first because i think it is easier to learn and do without thinking about. then start to learn to econimy pick. this way if your econimy picking fails you can fall back on alternate picking which works in most cases.


as for the name econimy picking, its sort of a hybrid between sweep picking and alternaye picking. i have only ever heard of it by this name.