The Partner Programs are shown here in this screenshot of Thomas Parkinson's Detail Page.
The first level of search occurs if a user of any one of the programs searches directly for an individual using user-entered search terms in the default fields. For example, if I go to one of the programs and click on their default search screen and start putting in names, dates and places, each of the programs then produces a list of results. Although the four programs vary somewhat in the perceived accuracy of the results of a manual search, it takes some degree of skill and persistence to see more than the most common types of records. This type of search considers all of the collections (presumably) on the website.
Better results can be obtained by searching in each of the programs directly into a specific collection of records. For example, if I choose one U.S. Census year to search, my ability to find my ancestor increases. Each of the programs allows you to search an individual collection, although the definition of a collection varies from program to program.
In both of these manual searches, the results may produce such a large number of individuals as to appear to be inaccurate, even if the there is, in fact, a high degree of inaccuracy. The average user interprets a long list of results as inaccuracy. On the other hand, if a search returns no results, the average user immediately assumes that the website has no pertinent records, when in fact, the user's search terms may not agree with the content of the records. For example, if I do a user-generated search, I may enter the name as I assume it to be recorded say in English, when the records have the name in the person's original language. Only MyHeritage.com has addressed this particular issue by translating name searches into different languages. Even with name translation technology, a manual search will only produce entries that match the search terms. If I am searching for John Jones and the ancestor's name was really Robert Jones, my searches will not likely find the correct information no matter how efficient the search engine may be.
Each of the four programs also provides an automated search for record hints for entries in a user submitted family tree. These have proved to be very accurate because they go well beyond the capabilities of a user to enter the same information used by the programs to make a search.
Going back to the links in the Family Tree. Each of the four programs provides a mid-ground search capability, more accurate than a user entered search, but still not as accurate as the automated record hints. In each case, the programs use the information entered into an individual's detail page to make the search. So, for example, if I am search for Thomas Parkinson above, I can click on each of the four links and have the programs use what is present on the detail page to search for my individual. In this case, the accuracy is likely better than if I just enter data, but the results of any search will still depend on the accuracy of the information I have in my family tree.
In the end, a search using the links to each of the four database programs will likely produce results that are better than simply searching for an individual by typing in search terms in search fields, but perhaps not.
There is another issue, of course, and that is that the person using the search links does not have a subscription to one or more of the programs. That will prevent a full utilization of the results and will very likely result in a suggestion that the user subscribe to the program. Why would anyone be surprised at this result? Three of the programs are fee based and it would not be a very good practice to allow full access to the programs merely because a search was made from FamilySearch.org.