The federeal grants of land were gifts which involved real state properties and were made by the US goverment to certain recipients. During the 19th century, most of such concessions aimed to favour the development of the railroad system.
Grants-in-aid constitute sums of money delivered by the central goverment for conducting a specific project. Money can be delivered to a state or local goverment, and also to individuals. It is not a loan hence it does not require repayment but the money needs to be spent according to predefined guidelines.
The reason for the generalization of the grants-in-aid model along the 20th century, was to enhance the degree of control of the productivity of such public investments. This format allowed to know in detail how the public assest (money) would be used rather than making concessions and waiting for the results, giving total freedom to the recipients but without any guarantee of his performance.