Send for: You can use "send for" two ways. The first way is the same as your first definition. You are summoning someone to come or sending someone to fetch them. However, if you say "send for" you are indicating that you are in a position of authority over the person you sent for. (This is American English) A general can send for a soldier. A boss can send for an employee. A parent can send for a child. However, the phrase has a harsh undertone to it, like you are ordering this person around. It can sound like you are angry at the person you are sending for. And you probably would not want to use the phrase when talking about a friend or someone in authority over you. Just be careful when you use this phrase. "I sent for Tom" just sounds a bit arrogant. "I sent Jane for Tom" is less so. When in doubt you can always say something like: "Jane is going to ask Tom to come." or "Jane went to pick up Tom" These phrases sound friendlier. (Especially if Tom is your friend or your boss.) The second usage: "Send for" can be used when referring to ordering something by mail or internet. "I sent for some candy." "I sent for a new sweater." In this case, the phrase is neutral and can be used when referring to any order.

Your first response is correct.