alike vs. the same:
"alike" means similar, so not 100% the same (although some people do say "we look exactly alike" to mean "we look exactly the same")
a lot vs. many:
Same meaning but "a lot" can also mean "very much". For example: "I like you a lot"
wish vs. hope:
This one isn't easy. "wish" is a little bit like praying, wanting something in the future or past to change.
- I wish you didn't do that. - You did it and I'm unhappy about it. I would prefer if things had gone differently.
- I hope you didn't do that. - I don't know whether you did it but I have a preference about it.
But then "I wish you a good day" and "I hope you have a good day" are more or less the same.
a little bit vs. few:
If you mean "a little bit of", then it's used with uncountable nouns, whereas "few" is with countable nouns: "a little bit of time" or "a few minutes"
Otherwise, "a little bit" is used like this: "I like you a little bit"
may be vs. perhaps:
I guess you mean "maybe". In this case, I think they are more or less the same. But "may be" and "maybe" are different.
sick vs. ill:
As verbs, it is hard to explain the differences. It depends on the problem.
say vs. tell:
Usually, you can say "say [sth] to [sb]" or "tell [sb] [sth]", but we normally use "tell" with a person.
- Say my name.
- Say my name to him.
- Tell him my name.
Also, "tell" implies it is something they don't already know.