“收集”，东西是现成的，只需要把它们聚集在一起。 The things is ready-made,what you need to do is only gathering them together. “采集”=采摘与收集，一般用于一些植物或水果的采摘与收集，也常引申用于一些科研数据的“测量与统计”，相比“收集”，它的东西不是现成的，还需要付出努力进行一定的预处理。 采集 is to pick and gather,it's often used for picking and gathering plants or fruits,or measuring some scienctific research data and keeping statistics.Coparing to“收集”,the things you are going to 采集 is not ready-made,which means you have to work hard to do some pretreatment before you gather them.
In Chinese, they are synonyms and, in essence, both mean "to collect, to gather together". The only difference is that the nouns that follow are different. For example, collect data=收集资料； collect waste=收集废品； collect specimens=采集标本 In my opinion, I think there is no logic to distinguishing them, but everyone is told to use them in this way. You have to memorize which one to use in what situation.
For information see Chinese dictionary 【收集：使聚集在一起：～资料｜～废品。】 【采集：收集；搜罗：～标本。】