The number of scholarships that may be offered (varying by the governing organization and the division) is limited by the governing organization itself (NCAA, NAIA, or NJCAA). As that is the case, no school within the same division could offer more scholarships (in total) than this limit. However, each school's athletic department could potentially budget less than the maximum allotment to swimming specifically. Swimming is considered an "equivalency" sport, which means that the limit of scholarships (in total) may be distributed to as many athletes as each program desires, so it is much more common for schools to offer partial scholarships to a larger number of athletes. Here is a link to a great reference summarizing this information (Swimming Scholarships in College). The bottom line is that the number of men's swimming scholarships offered at a college/university will be dependent on budget and the talent level of the "pool" of incoming recruits, which could vary from year to year.
When colleges offer swimming scholarships, they do so based upon their needs, considering the likelihood of recruits to make the team more competitive at every stroke and distance. Therefore, from the perspective of the individual swimming recruit, the ability to obtain any scholarship money at all will always be based upon comparative athletic ability (times) and the likelihood of the swimmer to score points in competition for the prospective college team.
It is relatively easy for a swimmer to determine how attractive he/she would be as a recruit. Almost all college swim programs will post a list of their recent best times (not the all-time records) on their website. If the swimmer's times for a given stroke and distance are within the top 3 recent top times, that swimmer could likely score points for the college team. If the swimmer's times are near or better than the current swimmers on the college team, or if the current top times are held by seniors who will be leaving the program, there is a greater possibility of being offered a scholarship.