When a company reimburses you, it means you have paid money to do something and are given back a portion of that money at the end of the task. For example, you pay $1000 for a plane ticket and the company reimburses you $600, therefore you only pay $400 total for the ticket. The exchange of money happens twice here. You first paid $1000, then are returned $600. When a company subsidizes you, it means they will cover the cost of something immediately, therefore making it cheaper. For example, the company will subsidize $200 for your plane ticket that costs $1000. Therefore you will only pay $800. The exchange of money happens once here. You pay $800 for the plane ticket because the company has made it cheaper by $200. The example sentences you have provided work well. To understand the difference, think about how the money is being handled.

Common uses for these words 1) Thanks for paying for my meal. I can't believe I forgot my wallet. I will reimburse you on Monday. 2) Her uncle subsidized her entire trip to Australia. She is his favourite niece. He thought of it as a graduation gift. Hope this helps