As we know "hold" is sujetar, sostener or agarrar buy using "hold me" or "hold me tight" like The Beatles song, it would be like "abrazar a alguien fuertemente" or "un abrazo de oso" as we say in Spanish. And "hug me" is like "abrazar normalmente" That's what I understand of it, so kind of hoping it helps you abit but let's see what a native English/Spanish speaker says. :)

To be 'held' in this case usually means some longer-lasting form of physical comfort, an extended hug to relieve emotional distress or provide comfort. Hugging is usually more short-lived, a form of greeting between people who may not be close at all. In America, where we have huge personal space, 'to be held' also implies a physical closeness that may not exist with hugging, which is why the phrase 'hold me' is usually only said to very close friends or boyfriends/girlfriends/spouses.

'what is the difference', not 'which is the difference' hold me= asking the person to hold a part of your body, commonly hand. hug me= asking the person to hold your entire body, wrapping their arms around you.