Open source describes a pragmatic projection of the four software freedoms - to use, study, modify and distribute software for any purpose. As I have explained before, people who find value from the software synchronise the fragment of their activities which relates to the software in question in a community of others with related fragmentary needs (but without a necessarily related motivation behind it). The community is of equal peers, with no one participant necessarily benefiting more than any other. True open source communities are "open-by-rule" - they have a governance that ensures no single community member can exploit the others.
Crowdsourcing describes the leveraging of the marginal interest and free time of a large group of people to complete a task that otherwise could not be economically completed. The result typically benefits the initiator hugely, without significantly compensating the participants. It's one of the examples of crowd behaviour James Surowiecki cites in his very interesting book The Wisdom of Crowds.
The new US web phenomenon Kickstarter is a modern example of crowdsourcing. It allows entrepreneurs to pitch their wild idea on the web site, and then offer token rewards in return for donating money to pay for bootstrapping - or in some cases fully executing - the business in question. The web site's denizens pledge relatively small amounts of money and in return get token items - in some cases samples of the product to be created, in others just mementos - in the event that the project is fully funded. Importantly, they get no stake in the business that's created. They are not "investors" - they are instead crowdsourced donors, not even benefitting as much as sharecroppers.
This is not to say I think crowdsourcing in general is a bad thing. I am for example rooting for Christopher Salmon to get fully funded today for his proposal to create an animated version of Neil Gaiman's "The Price", and have pledged a small amount towards it because I'd like to see it exist. But it's not the same thing as open source, where a community comes together for their collective mutual benefit and remain co-equal stakeholders.
As Henrik Ingo explains more colourfully, there are some businesses that don't understand this, and exploit community for their sole benefit in the name of open source. But you may by now have figured I don't have a high opinion of that approach!