An "At Source Deal" means that the percentage of royalties paid to the publisher is based on earnings in the country where the royalties were generated, i.e the source where the royalties were generated.
A "Receipt-Based Deal" means that the percentage of royalties to be paid to the sub-publisher is based on earnings in the country where the payment was received, rather than where it was generated.
For example, lets say that your US Publisher is working with A French publisher to collect earnings for a song currently generating mechanical royalties in France. Lets say that this song has generated $100 dollars in royalties in France (or 'at the source').
If you have signed into a 'Receipt-based Deal' with your US publisher, then they will pay you whatever royalty percentage you are owed from the amount they receive from the French publisher (the French publisher first takes their cut, and then pays the rest back to your US Publisher). So, if you signed into a 75/25 deal with your US Publisher, and your US publisher has agreed to a 75/25 sub-publishing deal with the French publisher, in the end you will get 75% of 75% of the original $100 dollars earned at the source. In other words, you would earn $52.25 dollars out of the $100. Essentially while your agreement with your US publisher is 75/25, everywhere else it is essentially 56.25/42.75 since the US publisher signed a 75/25 sub-publishing agreement.
However, if you signed into a "At Source Deal" with your publisher, you maintain the same contract percentage (75/25) wherever in the world you are earning royalties. In this situation, with an "At Source Deal" you would earn $75 out of the $100 earned in France since you take your cut at the source of earnings, before any cuts/deductions to sub-publishers are made.