Is the 45-day exempt visa issued at airports and land borders in Thailand?

It all depends on how long you stay in the other country. If you are actually being a tourist, and visiting the other country to explore it, no problem, but if you are repeatedly entering and just turning around and re-entering Thailand, you will have real problems from the second time on, with being refused entry usually on the third attempt.

Any visa exempt entry by March 31st will be stamped in for 45 days. After that it's back to 30 days. It doesn't matter how you enter.

But you can only enter Thailand visa exempt at a land border 2 times per calendar year.