Structure of proteins
primary structure
focus = peptide bonds (because these link the amino acids
The sequence of amino acids, for example AGGVHIL..

secondary structure
focus = H-bonds between the parts of the backbone
 There are several different types of secondary structure (α-helices, β-sheets, etc.). However the most import thing to remember is that the secondary structure refers to the the patterns of hydrogen bonds formed between amine hydrogen and carbonyl oxygen atoms contained in the backbone peptide bonds of the protein



your confusion
You are partly correct from a very simple perspective you can see the secondary structure of β-Sheets just as connected primary structures. However when talking about a piece of secondary structure you have to take the hydrogen bonding into consideration as this is what connects your primary structure parts (β-strands) to form a β-sheet.