Let me start by saying that there is no one fixed way of translating job titles. My remaining business card collection of people at listed companies numbers well over a thousand meishi and there is significant variation in all kinds of titles.

The titles you mention are all based around 取締役 - directors, hence the short form 取 - with additional titles tacked on and the whole thing contracted for the sake of brevity. The 取締役 label has legal implications so it is important.

The 執 could be either 執行役 or 執行役員, which are not in legal terms the same thing. Fortunately, both are usually rendered with some variation on "Executive Officer". I've just been looking at my collection and I see a couple of 取締役 常務 執行役員 of listed companies, for example. One is translated as "Director of the Board & Managing Executive Officer" in an attempt to combine the 常務 "managing director" concept with the 執行役員 or 執行役 but I would say a simple "Executive Officer" is far more common.

Because there are so many quirks in job titles and because it's a sensitive area, you should try to establish the full version of the original Japanese title. Such information can often be found in the annual report or the yuka shoken, at least for the major directors. If translated English versions exist by all means use them!

取専執 -> 取締役 専務 執行役 (or 執行役員). Semmu is usually translated as "senior managing director" to distinguish from Jomu (below).
取常執 -> 取締役 常務 執行役 (or 執行役員). Jomu is often translated as "managing director". As per the subject line of this answer, I would go with Managing Director & Executive Officer.

(NB: it's possible for companies have multiple people of the same nominal rank.)