As you stated, the Shulchan Aruch Yoreh Deah 116:2 forbids the consumption of meat and fish products together, out of concern that it is unhealthy. Since this is a health issue, it should apply to all types of meat and fish. I say this because, if it only applied to certain types of fish and meat, then the Shulchan Oruch would have specified the cases in which it applied and those in which it did not.
I found a full discussion of this subject in Fish and Meat by Aryeh Leibowitz
Regardless of the origin of the prohibition, gemara Chullin 9a states
explicitly that one must treat dangerous activities with greater
stringency than one would treat halachically prohibited activities
Thus even though (as quoted below) the prohibition may not apply in our day, or may only apply to the specific fish mentioned in the gemoro, we still should refrain from mixing any type of meat and fish.
It should be noted that recent research has found that stearic acid
found in beef may actually lower LDL cholesterol (See American Journal
of Clinical Nutrition 1994;60 (Suppl) : 1044s). On the other hand fish
contains eicosapentaenoic acid which has been found (paradoxically) to
INCREASE lipid peroxidation (J invest dermatology 1994;103:151; Intl J
Vitamin Nutrition Res 1994;64: 144; Journal of Nutrition
1992;122:2190; Journal of Lipid Research 1991;32:79). In addition
there may be an interaction in the liver (P450) between stearic acid
and eicosapentaenoic acid. This being said, there is no evidence to
indicate that drinking some schnopps in between would in any way solve
this problem.
The opinion of Magen Avraham. The Magen Avraham (Orach Chaim 173)
writes that there are many natural phenomena mentioned in the gemara
that simply no longer apply today. The health concern of eating meat
and fish is simply another example of something that used to be a
real concern, but is simply no longer an issue. Perhaps this can be
supported by the fact that the Rambam omits this concern from his
Mishnah Torah entirely. The Chatam Sofer (Responsa 101) offers two
explanations for the omission of the Rambam. First, he suggests, it
is possible that the Rambam knew that the gemara was only concerned
with the specific fish mentioned in Pesachim 76b, but all other fish
really pose no danger when mixed with meat. Alternatively, Chatam
Sofer suggests, the Rambam knew that nature has changed and although
there one was a legitimate health threat posed by mixing fish and
meat, no such threat exists today. (It is important to note that
Chatam Sofer does not recommend that we rely on the Rambam’s opinion
in this area.)