An equation is an equality which is satisfied by a unique set of values of your variables. You have, after the #=# sign a fixed value, a fixed result.

For example: the equation #4x-2=0# has zero as result and only #x=1/2# as solution; this means that if you substitute the value of #x=1/2# in the equation you have the result zero, i.e., the equation is satisfied.

Now, a function is similar, the only difference is that now you can have a lot of results after the #=# sign and so you can have a lot of solutions.

For example: the function #4x-2=y# doesn't have a definite result (as before that was zero) but another variable #y#, so every time you choose an #x# you'll get the corresponding value of #y# that satisfies it.

If you choose:

#x=1 -> y=2#

#x=2 -> y=6#

....etc.

If #x=1/2 -> y=0# which is the solution that we found before for our specific equation (in which the #y# was already set as zero)!

So to summarize, an equation has a fixed result (after the #=# sign) and an unique set of solutions (values of the variables); a function can have a lot of results (possibly #oo#) and, as a consequence, a lot of solutions.

hope it helps