What is the difference between a manager and a coach in case of a football team?

The short answer is that these 2 terms have equivalent meanings in football. And whenever you read one of these words in a sports article, most of the times, authors don't distinguish between terms and don't emphasize any specific meaning.

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The long answer is that the term "manager" is frequently used in the UK to distinguish between a "normal coach" and a "a coach who also has responsibilities of a sporting director (director of football)" - a "manager". In continental Europe, however, the terms "(head) coach" or "trainer" are more prevalent, and in addition, many clubs have explicit sporting director positions.

The exact difference can be best understood by reading Mauricio Pochettino's explanation:

If you are the manager, you decide many things about the club. But if you are a head coach, your responsibility is to play better, try to improve the players and to get positive results.

At Southampton, I was a manager. My responsibility was not only to coach [train] the team. With Tottenham, I am a head coach. A head coach is head of your department. My department is to train the team.

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But again, the main difference is that in the UK, people use "manager" and in the rest of Europe, people prefer "(head) coach". Here are the demonstrative examples from official websites of some biggest clubs:

• Zinedine Zidane - Real Madrid - not UK - "coach"
• Ernesto Valverde - Barcelona - not UK - "coach"
• Massimiliano Allegri - Juventus - not UK - "head coach"
• Jupp Heynckes - Bayern Munich - not UK - "head coach"
• José Mourinho - Manchester United - UK - "manager"
• Jürgen Klopp - Liverpool - UK - "manager"

As you said in question these terms are used interchangeably. From Wikipedia:

In association football, a manager is an occupation of head coach in the United Kingdom responsible for running a football club or a national team. Outside the British Isles and across most of Europe, a title of head coach or coach is predominant.

and also,

The title of manager is almost exclusively used in British football. In the majority of countries where professional football is played, the person responsible for the direction of a team is awarded the position of coach or "trainer". For instance, despite the general equivalence in responsibilities, Bobby Robson was referred to as the manager of England, while Joachim Löw was described as the head coach of Germany (Germany also has a team manager role that is subordinate to the head coach and that is filled by Oliver Bierhoff).

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However, the difference between these terms can be understood as:

A manager is a part of a football team who has complete authority over the running and functioning of the team. He has the autonomy to choose his supporting staff, along with the provision to add players to the team if he deems it necessary.

and, a head coach is only given the responsibility of ensuring his team putting a good performance in the match they are playing. That includes the likes of choosing a first team and training the players in specific sets of routines required for their position in the team. The management of the team is under the club board.

Tottenham Manager Pochettino, in his interview accurately put what the difference is in the two roles^{1, 2, 3}.

Pochettino has explained: “If you are the manager, you decide many things about the club. But if you are a head coach, your responsibility is to play better, try to improve the players and to get positive results.

“At Southampton, I was a manager. My responsibility was not only to coach the team. With Tottenham, I am a head coach. A head coach is head of your department. My department is to train the team.”

Also, when former Sunderland head coach Paolo Di Canio got sacked after just 13 games in charge in September 2013 . He stated illustrating differences between roles of these two:

“Not one of those [players] was bought by me. Roberto De Fanti and Valentino Angeloni were the two responsible for that technical error, with the maximum support from the chairman, which is Ellis Short. But I didn’t bring in one player. I asked for them to bring in 80 per cent British footballers.”

At last, many websites^{1, 2} even premierleague.com use these two terms interchangeably and shows Antonio Conte as a manager of the club Chelsea F.C., while the official website lists Conte as a head coach.

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_{For comparison against manager considering coach as head coach.
What's the difference between a coach and a manager?
Football (soccer) :What is the difference between football coach and football manager?
Antonio Conte asked who Chelsea will sign... here's his response}

Great distinction between the two roles of Manager and Coach. Take aways are that Manager has overall Strategic responsibility for the Club's affairs reporting to the Board. The Coach's role is more Tactical, focusing on mental / psychological and physical preparation of the team for optimum performance as a system or unit, to the specific tactics needed against a specific opponent This would include individual fitness and skill development of each player, as well as ensuring that there is a coherent (scientific) system of play, which ensures the best results, being mindful to identify the best positional placements on the field, also drills for attack and defence, as well as winning and recovery tactics, planned and executed in conjunction with the Manager. The coach must have capacity to stand in for the Manager, in the event that the manager is absent.

These two roles would ideally be supported by such functions as the Team Medic, who ensures optimum health of the team, and attends to players in recovery from injury; also a Team Psychologist for morale boost, to build mental toughness at both individual and Team level, so that they can outlast their opponents, or bounce back when forced onto their book foot..