家、学、教 were used after names of religions depending on the person / what they wanted to emphasize. Take for example Confucianism that can be called 儒家、儒学、儒教. Taoism that is 道学、道家、道教。Buddhism is 佛教、Islam is 回教。The rule of thumb is that 教 puts more emphasize on the religious aspect , 家 on the "family" (literaly), which can be understood as the school, and 学 on the way of learning. You can also use the word 思想, which means thoughts (and you get things such as 儒家思想）, and others ... But I would say that what we could consider the closest to the "philosophy-religion" is the suffix 教.