Symbol = element
Formula = compound
A chemical symbol is used to show an element which is not combined with any other elements. I'll list some examples.
H = hydrogen
He = helium
Li = lithium
N = nitrogen
Na = sodium
Notice that symbols can have 1 or 2 letters. The first letter is capitalized, the second must be written with a lowercase letter.
A chemical formula gives the type and number of elements which are found in a chemical compound. Here are some examples.
CO = carbon monoxide (carbon with oxygen)
NaCl = sodium chloride/salt (sodium with chlorine)
Here are a couple videos to help with writing chemical formulas.
Hope this helps!