Hello Steve,
Here is my answer.
집다 = to pick up or hold something which is on or in somewhere (ex. Sth on a table, sth in a box, sth on a plate or on the floor, and etc.)
As your friend explained to you, '집다' can be described a 'to pick up sth by using chopsticks or forks or by hand'.
Ex. 음식에서 콩만 집어 내지마. = Do not pick up the beans in the dish.
책상 위에 있는 펜 좀 집어줄래? = Can you pick up the pen on the table and pass it to me.
줍다 = to pick up something on the ground level.
Ex. 바닥에 있는 가방 좀 주워줄래? = Can you pick up the bag on the floor?
그 펜 좀 주워줄래? = Can you pick up that pen? (assuming the pen is on the floor)
When you '집다' sth, you are holding sth after picking it up and when you '줍다' sth, you pick up sth and that is the end of the action.
Ex. 나는 바닥에 떨어진 펜을 집었다. = I picked up the pen on the floor. (And now I am still holding it by hand.)
나는 바닥에 떨어진 펜을 집어서 책상 위에 놓았다. = I picked up the pen on the floor and put it on the table. (The pen is on the table now.)
나는 바닥에 떨어진 펜을 주웠다. = I picked up the pen on the floor. (I'm possessing the pen but not holding by hand right now.)
나는 바닥에 떨어진 펜을 주워서 책상 위에 놓았다. = I picked up the pen on the floor and put it on the table. (The pen is on the table now.)
Hope it helps! )
Ex.