Some years ago, an online content creator formulated a theory about how every Adam Sandler movie is part of the same connected universe. Their explanation warranted credit because the evidence was there. So, when an eagle-eyed viewer noticed that Sandler's film, 50 First Dates, included the name, T.B. Callahan of Callahan Autoparts, fans jumped to the conclusion that it, too, connected to another comedy-centric universe.
For clarification, Callahan Autoparts is the featured auto-parts company in Tommy Boy. The 1995 comedy starring Chris Farley and David Spade centered around the pair driving around the country, selling brake pads, in an attempt to prevent their manufacturing plant from shutting down. Farley's character, Tommy Callahan III, succeeds in the end, presumably pushing the company into an era of prosperity. That's partly the reason fans believe the Callahan Institute in 50 First Dates references the auto-parts plant from Tommy Boy.
Unfortunately, there's been some confusion surrounding the quote-unquote connection. Akroyd's character mentions a character named T.B. Callahan, and no one in Tommy Boy has those initials. Farley's character is T.R. Callahan, and Brian Dennehy's character is known simply as T. Callahan Jr.
It's worth mentioning that Dennehy's character is referred to as "Big Tom" throughout the film, but even those initials don't line up with the T.B. Callahan reference in 50 First Dates. Perhaps Dr. Keats (Akroyd) mixed up the initials. He was working at an institute for people suffering from memory issues; maybe Keats was also a patient.
While never confirmed, Peter Segel likely chose the names of T.B. Callahan and Callahan Institute as a small homage to the 1995 movie. Tommy Boy is praised as one of the best comedies of the 80s and 90s, so there's logic behind Segel referencing it in 50 First Dates.
Another reason the placement of Callahan seems intentional are the inadvertent references to other comedies. Segel also makes Rob Schneider's character an assistant to a marine biologist. That may not appear significant, but the occupation isn't that different from his character in Deuce Biggalo: Male Gigolo. They both care for aquatic creatures, after all.
Additionally, Sean Astin's character portrays a quasi-meta version of Rudy—one of the first he portrayed on the big screen. The thing is, instead of using willpower to excel in sports, Astin's character resorts to "juicing." Rudy doesn't go to such lengths, which is why Doug (Astin) going down that avenue is funny for all the wrong reasons.