训练 = train for example, the coach of all kinds of sports "train" their players. here we use 训练 so 训练 is a verb for something physical BUT we can use 训练 for something NOT physical but very hard for example, "study" or "learn"---student . for example, 让老师好好训练训练你，你就能考好了 let your teacher 训练 you, then you can get better note. 培训 is a verb for something about "brainwork" and about "skill of job" for example, 这个学校可以培训老师-----this school can 培训 teachers (it means the teachers can improve their skills about teaching in this school) AND 培训 and 训练 can be used as nom too for example 参加培训 or 参加训练

培训主要是指头脑方面的用培训，训练主要是体力上的用训练。

培训 actually more likely to be used  when you get a train for Intellectual work like how to be a manager or how to study,while 训练 suggests some physical train like P.E.