Difference between a "movement" and a "campaign"

Solution 1:

The meanings overlap, obviously. Here's Arlo Guthrie's take on it in Alice's Restaurant...

You know, if one person, just one person does it [the psychiatrists] may think he's really sick and they won't take him.
And if two people, two people do it (in harmony), they may think they're both faggots and they won't take either of them.
And if three people do it, can you imagine, three people walking in, singin' a bar of Alice's Restaurant and walking out? They may think it's an organization.
And can you, can you imagine fifty people a day,I said fifty people a day walking in singin' a bar of Alice's Restaurant and walking out? Friends they may thinks it's a movement.

I'm sure even after almost 50 years, more than 50 people a day sing a bar of Alice's Restaurant (though probably not in psychiatrists' offices! :). The point is it could be classed as an organisation (or movement) simply on the basis of many (or very many) people acting in a "coordinated" way.

But in order to be classed as a campaign, a "movement" would need to have one or more specific goals. Normally, goals which can only be achieved by appealing to others whose support is vital to the advancement of "the cause" (sense 2 there).

In short, for those specific contexts where the two words overlap, to the extent that they might be used with slightly different senses (bearing in mind that very often, they're not), that difference primarily hinges on the implications of OP's two definitions. People in a campaign know (and usually publicize) what they're trying to achieve. People in a movement are simply like-minded (but may not be very clear - or even consistent - about what if anything they want to change).