I usually see abide used with rules in English. For example:
"He always abided by the rules and never broke them." = He always followed the rules.
Tolerate, on the other hand is more complex. When we tolerate something or someone, we allow that thing or person to be just how it is. We accept that the condition is how it is. We might not like it, but we tolerate it.
"He didn't like history class, but he could tolerate doing the homework." = He didn't like the class, but he didn't mind doing the homework.
I hope this helps! If you have the original sentences where you saw these two words used, you can always post them here!