Counting days 101?

Is it just me or does anyone else see no difference between 1 and 2? In both cases the vacation starts on March 14th and continues for 10 days?

I would expect the vacation to begin on the 13th and end on the 22nd. Meaning her last day of work would be the 12th and she would be back on the 24th. But I also would not expect her to get the numbers exactly correct and it would all just be estimate estimates. It would make the most sense for her to take a NINE day vacation and I would be able to look at a calendar and see her vacation go from Saturday to the next Sunday (and she would only miss five days of work).

The way the other person has phrased it is ambiguous and implies an approximation. The problem isn’t anything to do with English; no English speaker would be sure of the meaning just based on what has been said.

These things are difficult to understand in any language.

It's ambiguous, but I'd probably interpret it that day 10 is the day the vacation starts. If the vacation is in one day, it's tomorrow. If it's in two days, it's the day after tomorrow. Continuing on in that vein, his vacation would start on March 13. In reality, I'd ask him for clarification.

I think most people will mean that on the tenth day, they will be on vacation. So in your example they will be on vacation on the 13 th through 22nd. They would return to work on the 23 rd.

Unrelated to the question, but "methinks" is archaic English from like the 1500's (Shakespeare etc.) We occasionally have phrases in English where it is used (usually for comedic effect), but no one has actually used it in daily speech for hundreds of years. :)

I would assume she work on March 12 and March 24 but not any of the days between those two dates. It’s a somewhat unclear statement without specific days mentioned, and I would personally ask for clarification if something like this happened IRL.

I think the confusing part to Americans is what’s a 10 day vacation

(American) Depends on whether they mean consecutive days of vacation or work days of vacation. If I tell you I'm leaving Friday afternoon and taking 10 days off, it likely means I will be gone two full weeks (M to F, then M to F again because I'm using up 10 days of earned vacation from work). If I tell you I'm leaving Friday afternoon for a 10-day cruise (for example), it likely means I am counting the weekends as part of the time, so I would be back the Tuesday after next. There's a reason our out-of-office messages usually explicitly state what day we will return. "I will be out of the office from March 3rd through March 10th, returning on the 11th." or something like that. Because saying "I'm taking X days of vacation" isn't automatically clear.

There’s really no way of knowing just based off of the information he gave you

Yes, there's some room for ambiguity and confusion, but that doesn't mean we can't make a pretty good guess at what she means. 10 days from March 3rd is March 13th. You don't ordinarily count the current day when saying "in X days." i.e. if I say "in 2 days," I don't mean tomorrow. A 10-day vacation means that her vacation itself lasts for 10 days. If she is leaving on vacation on the 13th, that means she will be on vacation through the 22nd (and back at work on the 23rd). Could she have meant that she will be leaving on the 14th? Sure. Should you ask for clarity if that detail is important to you? Of course. But the above interpretation is what I would describe as a standard understanding of those phrases.

I'd just ask when their last work day is or when they'll be back. This would clear up any confusion and guesswork.