「会社員(かいしゃいん)」:An company employee. (an occupational classification)
e.g.「会社員(かいしゃいん)」,「医者(いしゃ)」,「教師(きょうし)」, 「エンジニア」and「銀行員( ぎんこういん)」, etc.
Use it if you want to simply say that you are a company employee.
e.g.私(わたし)は「会社員(かいしゃいん)」です。
「社員(しゃいん)」:employee of the company.
Use 「社員(しゃいん)」in conjunction with the company's name.
e.g.「私(わたし)はPanasonicの社員(しゃいん)です」
Not「私(わたし)はPanasonicの会社員(かいしゃいん)です」.
The word 「会社員(かいしゃいん)」 and 「社員(しゃいん)」are similar in meaning and sound, but there are differences. Pay attention to the differences and remember them.