I guess it depends on the person. At least during early war some Wehrmacht generals hated Waffen-SS for big losses due to aggressive war style. Later on I think many were happy to have Elite fighting force among them.
If you mean the SS I have read the einsatsgruppen followed the frontline troops and cannot say if the SS had much contact with the Wehrmacht in battle areas.
Heer was the regular German army. Wehrmacht was the entire German military, army, air force, navy. Since the army was by far the largest, Wehrmacht is sometimes used as if it meant army, but that is not quite accurate. This also shows up in the command structure: OKW (Oberkommando der Wehrmacht) was the headquarters for the entire military, with subordinate commands: OKH (Oberkommando der Heer) OKL (....Luftwaffe) OKM (...Marine (Navy))
There certainly was rivalry at the upper echelon but I wouldn't call it hatred. Now, when the SS was being used as a barrier force that executed deserters, they became hated. That job was ordinarly done by the feldgendarmarie (field police).
The German Army discipline code was quite strict. Soldiers for instance stealing food from the kitchen if caught were shot which sounds quite awkward. There were at times a guard in the kitchen at night and he could shoot at the soldiers getting in without permission. I could think they were shot after military court by own units men. I could be wrong but I would think such things took place rather often before example cases.
Just curious but read a long time ago that OKW By 1942 was responsible for all military theatres except the Eastern front against the Soviet Union. Also mentioned in wikipedia. Not sure about the details but perhaps Hitler wanted total control??
The Heer was the German Army of the Third Rech. The Army of the FRG is the Deutches Heer, as was that of the Second Reich. Heer (army) - Wikipedia. IRRC that Kurt Meyer in Grenadier occasionaly makes disparagong remarks about the Heer running away/ not pressing attacks because they lacked Faith in the Fuhrer..
I think it was Panzermeyer when in Greece 1941 he and his men were under heavy fire just to save and make his men move ahead he threw a grenade in the middle forcing the men run further. Or so he said.
I remember reading an account of an SS unit and a combined group of US Army and a Heer unit tangled at or just after the surrender. Apparently the SS had no qualms about shooting at the German Army. Not sure why they were shooting at each other.
I assume that what you're talking about is the Waffen SS. My readings lead me to conclude that at the highest level there was a somewhat concealed animosity. It was no secret that the Waffen SS were made to replace the Heer after the war. Had the Nazi state survived then there probably would have been civil war. At the troop level, no such animosity existed. They were fighting side by side against their foes. SS units baled out Heer units that were in trouble and vice versa. All these young men had the same dose of nazi propaganda growing up. Middle-level Heer commanders considered them "good comrades".
The Waffen-SS was the politically indoctrinated house force of the NSDAP and was intended as a counterweight to the Prussian-dominated Wehrmacht. It was supposed to prove the superiority of the Nazi ideology through successes at the front. In addition to an extremely pronounced esprit de corps, this also included a no less extreme brutalization: This was directed against everything that did not conform to Nazi ideology: In a speech in front of soldiers of the SS, Jesus was called the "bastard of a Jewish whore", which throws a telling light on the attitude of this force. In the end, the youthful idealism of the young men was deliberately abused: As one Wehrmacht officer described it, "They threw themselves away like hand grenades - not because they had to, but because they could." At the front, the Waffen-SS units were highly appreciated as neighbors, but there were always certain ideological animosities until the end. A little noticed aspect is that with increasing losses the racial aspects were more and more neglected and the Waffen-SS turned into an international force, which even had Muslim units.
It's a little more complicated Stug. Here's my understanding: The Schutzstaffel-SS was made up of several groups. The Waffen SS was intended to be more akin to an elite Heer unit. The Allgemein SS (General SS) was involved in enforcing racial policies and general policing, not looked upon favorably by the actual combat forces Waffen-SS and Heer. Then you had the SS-Totenkopfverbände, (Deaths Head) they ran the concentration camps and were looked down upon by most everyone. Personnel from this latter group formed the 3d SS Panzer Division Totenkopf, which served in the Waffen-SS. They were noted for their brutality and were responsible for many of the war crimes attributed to the Waffen-SS, though most Waffen SS divisions were involved in some war crimes/atrocities. Then there is the Einsatzgruppen, these were the SS units that followed the armies and massacred civilians. They were looked down upon by combat formations.
Read about the einsatzgruppen a long time ago. I was surprised that many men were hand picked and were often well educated. If you look them up from the Nuremberg trials in the net there are lawyers, architects, theology student etc. Not the brutal nazi believer you would expect.
The lines between the Heer and the SS were sometimes blurred. For instance, von Manstein for ever ruined his considerable military reputation when it came out that he actively supported the einsatzgruppen in his area. Other Heer commanders did likewise, but others actively opposed them-one even losing his life in the process. Many, while disapproving, took a neutral stance that it was none of their business as long as the gruppen stayed out of the area of actual operations. IIRC, the Heer was responsible for the area some 25 or 30 miles behind the front. Behind that, the nazi party took over.