in the US, if one's credit score has only recently improved within a very short time, would one be less likely to be approved than in the case where it had been at the current level for a long time?
Lenders care what your credit score is. They don't care what it was in the past. If the bank wants applicants to have a 700 credit score for a particular card, they don't care whether you've had that score for a day, a month, or a decade. They just care what your current score is.
As @NingNing points out in the comments, there are new FICO models coming out that incorporate more historical information about balances and payments into calculating your credit score. But banks will still just care about the current score not your score from last year.
Credit history can have a substantial impact on your odds of getting approved for a credit card.
Improved credit history doesn't guarantee you'll be approved, and previous poor credit history doesn't guarantee you'll be denied.
Understanding what range your score falls in can help you narrow the options as you decide which cards to apply for.
YES! They do matter. Asking yourself, "Why does my credit score matter?" For a lot of reasons, some of which you may not even be familiar with. A credit score is a way of distilling your relationship with debt down into a 3 digit number. It is used to evaluate your creditworthiness, or how likely you are to pay back the debt.
A Credit History is a record of your debts, payment history, and public records. Simply put, the length of your credit history is how long you've used credit. The length of your credit history, or how long you've been using credit, typically accounts for 15% of your total credit score.
I hope I have answered your question as simply as possible.