Is acetate and an acetyl group the same thing?

They are definitively not the same, if you could post your reaction, i can help you tell wich is formed.

an acetyl group is the folowing: CH3  -  C(=O)  -  R
that is  a methyl group bonded to a carbonyll group bonded to something, usualy an alkane chain.

Acetate however is CH3 - C(=O) - O - R
that is a methyl group bonded to a carbonyll group bonded to an oxygen atom, bonded to R.

this is a the general class of compounds called carboxylic acids...
......O
.......||
R - C - OH

this is a specific carboxylic acid called acetic acid
...... ...O
...... ....||
CH3 - C - OH

this is an ester.
.....O
......||
R - C - O-R'
where R and R' can be any hydrocarbon or substituted hydrocarbon.  and esters end in -ate...

this is ethyl acetate...
...........O
...........||
CH3 - C - O-CH2-CH3
the right part of the molecule, -CH2-CH3, is ethyl.  the rest of this ester is based on acetic acid.  Hence the name "acetate"

this is the general form of acetate group...
...........O
...........||
CH3 - C - O -

*************
this is acetyl...
...........O
...........||
CH3 - C -
it is not a carboxylic acid.. it's doesn't have that O on the right.

this is acetyl chloride.
...........O
...........||
CH3 - C - Cl...

********
the acetate and the acetyl group behave very differently.