Why is a dynamical system not a dynamic system? This is a research question in the history of math, I suppose.
As a non-native english speaker I became used to mathematical expressions like 'dynamical' and 'tangential'. When using them in daily conversation as substitutes for 'dynamic' and 'tangent' I got frowned upon by native english speakers who claimed to have never heard of these words before.
Some references suggest
https://www.merriam-webster.com/dictionary/dynamical
https://www.merriam-webster.com/dictionary/tangential
that indeed they can almost mean the same as 'dynamic' and 'tangent' but for some reason nobody seems to use these words that way.
So whereas in English:
A dynamic person-a dynamical system
the adjective is different
it is in French
une personne dynamique- un système dynamique
and in German
Eine dynamische Person - ein dynamisches System
the adjective is the same.
I am wondering when (and maybe also why) these expressions started deviating in English.
 A: Here are the two entries from Anthony Lo Bello's Origins of Mathematical Words (John Hopkins, 2013) which is very informative, entertaining, and perhaps curmudgeonly.  In his parlance, following the lexicographer Samuel Johnson, a "low word" is one with an "irregular combination" of roots that has "little or no etymological legitimacy."
dynamical  The Greek noun [dunamis] means power.  The corresponding Greek adjective is [dunamikos], pertaining to power.  The correct English adjective is therefore dynamic.  To superimpose the vestige -al of the Latin adjectival ending -alis upon the stem of a Greek adjective is often the product of ignorance and produces a low word.  In other cases, the addition of the Latin suffix to the Greek adjective is due to the fact that a different meaning is intended from that of the Greek adjective; thus, dynamic was an established word, so one spoke of dynamical systems rather than dynamic systems to avoid confusion.
tangential  See the entry tangent.  The Latin adjectival suffix -alis was added to the stem of the participle tangens, tangentis, which was already an adjective but felt to be a noun, the tangent.
A: Early uses of "dynamical" go back to the 19th century at least:

*

*On a dynamical theory
of gratings, Lord Rayleigh (1907)


*On the dynamical
theory of gases, J.C. Maxwell (1865)
Thermo-dynamical as an adjective was also common, see for example W. Gibbs's Thermodynamical Model (1900).
A: This is a subtle question of scientific jargon. Indeed, in everyday language, "dynamic" is preferred, and "dynamical" at most is seen as an awkward synonym. My feeling is that "dynamic system" would be the everyday language way of referring to a system that was actually changing in time, moving. Whereas a "dynamical system" in physics, mathematics and at least to some extent beyond is a system that by its nature is capable of exhibiting change in time, i.e., being dynamic; moreover, we make a statement about the reason for that capability, i.e., there is some description of what causes its specific dynamism. One distinguishes between a merely kinematical description and a dynamical description - a kinematical description merely addresses how something moves, whereas a dynamical description addresses why something moves (say, some variational principle).
Indeed, with respect to the latter sentence, there's a clear contrast: A "dynamic description" would be a description that itself changes in time; a "dynamical description" is one that explains the change in time of some other object that is being referred to.
A: Thing is, they do not mean the same thing. At least, not in theory.
Dynamic the adjective means "exhibiting continual change".
Dynamics the noun means "the study of forces and their relation to motion".
Dynamical the adjective means "relating to the study of dynamics."
A "dynamic" system is a system exhibiting continual change. A "dynamical" system is a system relating to the study of dynamics. (Since OP is Chinese, this is also why DS is 動力系統 and not 不定系統.)
Similarly,
Tangent the adjective means the geometric notion of touching but not intersecting.
Tangent the noun refers first to the geometric construct of the line tangent to a shape, and then also to the idea of "objects that can be split off without making a turn", whence the idea of "going on a tangent" when you derail the discussion with something related but not directly relevant. (You won't be going on a tangent if you change the topic or the direction of discussion abruptly.)
Tangential the adjective refers to the quality of "tangent". Hence you make a "tangential remark" while you "go on a tangent". Hence you look for "tangent lines" while compute "tangential forces". (The force itself is not tangent, but it is directly along the line that is tangent to the object.)

This, of course, gets muddled by the fact that English is perfectly happy with attributive nouns. English being remarkably loosey goosey about grammar for a Western language, understanding in theory why things are the way they are is probably much less useful than accepting their use as a convention. (After all, what is language but a convention to enable communication?)

Homework exercise: discuss transverse versus transversal
