「shake hands」と「hold hands」の違いは何?

Sometimes people tell me something like this:

"When I met him for the first time, he told me his name, and then we, uh... なんて言う... held hands?"

× He told me his name and then we held hands.
○ He told me his name and then we shook hands.

• hold hands（～と）手を握り合う［つなぐ］
• 表現パターンhold hands (with) (definition from Eijiro on the Web)
• shake hands 握手する、手を握る、合意｛ごうい｝に達する (definition from Eijiro on the Web)
• How should I shake hands? : どのように握手すればよいですか？
• Shake hands! : お手！◆犬に向かって言う表現

This evening I must have seen at least one hundred couples holding hands. There was a big Christmas tree, and an endless parade of couples, all holding hands, walked in front of the tree, took pictures, and then walked off hand-in-hand.

• 手を携えて (てをたずさえて) (exp) hand in hand; (definition from Edict)

Another woman sat at a table behind me. She had a box of Christmas cake on the table, but she looked really upset. She was waiting for a long time, made a phone call, and then walked away with her cake in a plastic bag. I wondered if she had been stood up.

• すっぽかす (v5s,vt) to stand (someone) up; to leave (something) undone; to neglect (a duty);

I suppose all that hand-holding was cute. It's still hard for me to think of Christmas as a romantic holiday, though. Where I grew up, that was saved for Valentine's Day.