Looking up...
She offered me a cup of tea.
She presented me with a cup of tea as a gesture of kindness.
to present something for acceptance or consideration
The company offered a bonus to its employees.
The company presented a bonus to its employees as an incentive.
Can be used in both formal and informal contexts.
a proposal or suggestion made to someone
He made an offer to buy the house.
He proposed to purchase the house.
Often used in business and commercial transactions.
Remember that 'offer' can be both a verb (to present something) and a noun (a proposal or suggestion).
'Offer' can be used in both formal and informal contexts, but it is often more formal than 'suggest'.
From Middle English 'offeren', from Old French 'offerir', from Latin 'offerre' meaning 'to present or bring forward'.
The word 'offer' can be both a verb and a noun. As a verb, it means to present something for acceptance. As a noun, it refers to a proposal or suggestion.