Loosely defined, a Faith-based college is one that identifies as Christian. Generally, you'll be able to tell that a college is Faith-based through their website, often found on the home page, but definitely through their mission statement and values. The term is inclusive of Christian colleges with both conservative and more relaxed standards.
While the term "Faith-based" applies to both conservative and relaxed standards and regulations, many Faith-based colleges lean toward less strict standards. For example, while both Christian colleges and Faith-based colleges may offer chapels, the difference between them may be that more strict Christian colleges require chapel attendance to a degree, while Faith-based leave it optional for students. Another example may be their code of conduct and what they expect from their students in terms of faith and living as a Biblical example.
Another difference could be faculty requirements. Some more strict/conservative Christian colleges may require that faculty be professing Christians, in alignment with the University's beliefs and values. Some more relaxed Faith-based colleges may not require faculty to be Christian, even though the college professes a Christian faith.
For the most part, the differences between conservative/strict Christian colleges and Faith-based colleges are subtle, but the faith is the same. What defines a Faith-based college is simply that: its identity of Faith.