We can credit Jim Shooter for developing the tense relationship which has come to characterize Captain America & Iron Man's interactions. Through the events of Shooter's "Korvac Saga" story, Captain America is nearly apoplectic about the state of Iron Man's leadership. Most of this tension came from the fact that Iron Man had not seen fit to share his secret identity as Tony Stark with any of the Avengers, Cap included. In Avengers #167 (1978), S.H.I.E.L.D. requests the Avengers' help in investigating a massive space facility (which proves to be the base of the Guardians of the Galaxy). Iron Man is late in arriving to join the team because as Tony Stark, he had been in conference with Nick Fury. Cap is boiling mad with Iron Man's tardiness: "You're sorry you're late? A hundred men might die up there and--" to which Iron Man sharply replies, "Then shut up and get into the ship!" The problem worsens when they reach the station and Cap instinctively assumes command, issuing orders to the others. Iron Man reflects, "It's no secret what Cap thinks of my leadership! I suspect his resentment is growing and getting personal!"
The very next issue, it exploded. The Avengers returned to their headquarters to find it invaded by one Henry Peter Gyrich, their new government liaison. Gyrich proceeded to read the Avengers the riot act for the many violations of government protocol they were guilty of. When Gyrich left, Cap finally unleashed what he'd been stewing upon:
"This team's been a pushover since you became leader! It's your fault... because you're treating your chairmanship like a part-time job! But that's what it is to you, isn't it? You're moonlighting as an Avenger, because you have a full-time job as Tony Stark's personal bodyguard!"
Iron Man began to respond cooly, answering that "all Avengers are guaranteed their personal privacy," to which Cap responded by punching him in his armor-plated face. "You low-life mercenary! Don't the Avengers pay enough for your services?" Now they were both angry, but before a real fight could begin the Scarlet Witch broke it off, shaming Cap by pointing out his own recent poor showings in battle. Cap sulked away.
Now that Shooter had turned up the tension, he almost immediately shut it back down. At the end of the day, Captain America and Iron Man were simply too reasonable to let this bickering continue. In Avengers #170 (1978), Iron Man confronted Cap in the Avengers gym and while Cap worked out, Iron Man confessed his own shortcomings: "I'm aware of my failings! I-I'll try harder, Cap... or, if you think I should, I'll step down! You can take over." Cap noted he'd "seen too many friends die in battle" and Iron Man was about to reveal his dual identity to Cap, but Cap cut him off: "Keep your secrets, Iron Man! You lead.. I'll follow -- that's enough!"
In Iron Man #125 (1979), Tony Stark came to Captain America for hand-to-hand combat training as he needed to go on a secret mission without his Iron Man armor. From Cap's perspective, he was simply helping the Avengers' financial backer, having no idea how much it meant to his fellow Avenger. Some time later in Avengers #216 (1982), Iron Man lost his armor while battling the Molecule Man, thus Cap and Thor both finally learned his identity. This knowledge almost immediately began changing Cap & Iron Man's relationship. In Avengers #224 (1982), Tony began dating the now-divorced Wasp. Wasp wasn't keeping a secret identity, but Tony went several dates without telling her the truth. After seeing them together in the tabloids, Cap confronted Tony, playing on his conscience. Cap noted her ex-husband Hank Pym was an old friend of his and it was unfair to do that to Hank - but likewise unfair for him date a teammate (also, Wasp was now the Avengers leaders) without her knowing it. Tony took the conversation to heart and gave up his secret identity to the Wasp; she immediately broke off the relationship.
Mere months later Tony succumbed to alcoholism and gave the Iron Man armor to James Rhodes. Cap and the Wasp tried to reason with him, but in his state that wasn't possible. He quit the Avengers, quit being Iron Man, quit running his company and soon lost his fortune. And despite all of this, Tony couldn't be reasoned with. In Iron Man #172 (1983), Cap found Tony living in a flophouse and tried to encourage him to return to his company before it was lost to Obadiah Stane, but Tony refused and ran away from both Cap and Rhodes, preferring to live in anonymity.
Eventually, Tony would reclaim his sobreity, reclaim his friends, reclaim his armor, reclaim his fortune and reclaim his company. Although Iron Man usually served on the Avengers' West Coast branch while Cap served in New York, the two remained good friends. That is, for a time.
Tomorrow! Iron Man goes to war!