Both countries keep the custom of giving to clients and to people who have helped you. The frequency, timing and manner of delivery differ.
Japan gives twice
Ochūgen (お中元) is the summer gift, sent generally in July in the Kanto region and generally in August in Kansai. The month shifts by region, so check where the recipient is before sending.
Oseibo (お歳暮) is the year-end gift, timed to arrive between early December and around the twentieth. If only one is sent, it is usually oseibo.
Their origins differ. Ochūgen descends from the Taoist Zhongyuan festival on the fifteenth of the seventh lunar month, later merged with Obon offerings. Oseibo grew from the year-end practice of carrying offerings to the main family house and the ancestors.
Usually shipped, not carried
This matters. Ochūgen and oseibo are normally ordered from a department store or online and delivered directly. Visiting in order to hand a gift over is now the exception.
Amounts are conventional too: roughly ¥3,000–5,000. Anything expensive puts the recipient under obligation.
Vietnam gives once, in person
Vietnam's quà Tết comes once, before Lunar New Year. And it is normally brought in person.
The gift matters, but so does the act of visiting. Calling on someone at year's end, meeting face to face, handing the gift over — that is the courtesy.
Hence the Vietnamese employee who proposes visiting a client before the year closes. The Japanese side tends to think shipping is sufficient; for the person proposing it, the visit is the substance.
More companies now refuse gifts
A modern caution: many companies now prohibit accepting gifts outright, under compliance rules covering anything received from a counterparty.
Vietnam has the same restrictions in the public sector and at large firms. A gift given in good faith can put the recipient in difficulty, so checking the other side's internal policy first is now standard practice.
In practice
For a Japanese recipient, check the region, time it, and ship it. For a Vietnamese recipient, make time for a visit before Tết.
More useful than copying the form is knowing which part is the substance in the other culture.