Are Quidditch teams restricted to 7 players in a squad?

Question

In CoS Wood comments before Quidditch practice

we should have won the Quidditch Cup last year...But unfortunately owing to circumstances beyond our control... p84, chapter 7

We learn Harry's reaction to this is that

Harry shifted guiltily in his seat. He had been unconscious in n the hospital wing for the final match of the previous year, meaning Gryffindor had been a player short and had suffered their worst defeat in three hundred years. page 84, chapter 7

However when Harry was given detention for wounding Malfoy and thus missing a Quidditch game against Ravenclaw, Ginny was drafted in as a replacement seeker.

Therefore what's the difference as to why a replacement was sought for one game and not the other? And furthermore is there not a Quidditch squad for each team in order to accommodate for possible injuries and suspensions to one of the starting 7?

Answer 1

Probably not always

As Oliver Wood explained, in at least one Quidditch match substitutes were brought in for exhausted players:

"A game of Quidditch only ends when the Snitch is caught, so it can go on for ages—I think the record is three months, they had to keep bringing on substitutes so the players could get some sleep."

—Harry Potter and the Sorcerer's Stone

It seems likely from this that professional Quidditch teams have proper backups.

Hogwarts is a different situation, but as indicated in the question, they at least have substitutes. As to why the team was a player short for the match in question, the explanation is probably simple: they did not have sufficient notification to find a substitute, or all potential substitutes were busy.

It seems possible that they did find a substitute, but still lost, because the substitute was not as skilled as Harry. This could still be consistent with calling them "a player short," since that might refer to the situation before they could find a substitute.

That said, in the Hogwarts Quidditch games, they do not seem to have a regular squad of substitutes,and instead must find them as the need arises.

For example, when Katie Bell ended up in the hospital, Harry had to find a replacement:

Katie Bell was still in St. Mungo’s Hospital with no prospect of leaving, which meant that the promising Gryffindor team Harry had been training so carefully since September was one Chaser short. He kept putting off replacing Katie in the hope that she would return, but their opening match against Slytherin was looming, and he finally had to accept that she would not be back in time to play.

—Harry Potter and the Half-Blood Prince

The unofficial replacement roster seems to be those people who performed well at the last tryouts.

One of the reasons why Harry would have preferred not to have to ask Dean to play was that he knew Seamus would not like it. On the other hand, he had to do what was best for the team, and Dean had outflown Seamus at the tryouts.

—Harry Potter and the Half-Blood Prince

Answer 2

They're not restricted in numbers, and do have reserves, at least sometimes. In Philosopher's Stone we have Lee saying

...a neat pass to Alicia Spinnet, a good find of Oliver Wood's, last year only a reserve... Quidditch

However, in Quidditch Through the Ages we're told

In the case of injury, no substitution of players will take place. The team will play on without the injured player. pg 28, 2001 version

so presumably reserves can only play if they know they're needed in advance of the match.

With only three matches in the year, which all count towards the Cup, it probably makes sense to spend time training their squad to play well together, rather than practising with different combinations of people that might never be used. Also, the matches for each team are spaced out (in PoA we know the first match takes place in October, and the final one just after the Easter holidays, so probably mid-April, Easter Sunday was April 3rd in 1994) so if you have enough notice of unavailability, you could train with somebody new.

In The Philosopher's Stone, Gryffindor had been struggling to find a Seeker — that's why they were so excited about Harry. They didn't have a secondary Seeker who could play. Harry confirms this before the match Snape plans to referee when Ron and Hermione try to convince him not to play

"There isn't a reserve Seeker. If I back out, Gryffindor can't play at all." Nicolas Flamel

For the final match, I presume they put a reserve in as a Seeker to have seven players on the pitch (or played with six and Harry didn't know the full rules). I'm not quite sure how they expected to win though — score lots of goals and hope the other team's Seeker caught the Snitch without doing the maths perhaps.