lay it out , spell it out

I will explain it in simple terms/in detail so that you will definitely understand.
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So they mean the same thing and are interchangeable?

For me yes:

Let me lay it out for you.

Let me spell it out for you.

Thanks, Optilang.

Yes, same meaning, but the connotations are different:
Let me lay it out for you. [as in presenting/spreading on a table

Let me spell it out for you. [as in spelling a word

Thanks, MH.

I don't think they're quite the same.

Let me lay it out for you - let me show you the whole picture, explain in detail what will happen. You didn't have all the information before, and now you will. (It's possible the person thinks you should have been able to figure it out for yourself, but it could simply be new information.)

While "let me spell it out for you" can have

Thank you, GG for the interesting insight. By the way, what's the meaning of little words? layman terms?

Simple words. Easy-to-understand words.

Thanks.