Is received check considerd as cash in accounting?

Welcome to Stack Exchange! My view is a little different than most. I will tell you my philosophy, so that you can decide what works best for you.

It depends on what the check is for.
IS it Cash On Delivery (COD)/Retail i.e. the exchange of product happens immediately. You give me the product and I give you the money -> cash.

Is it Cash In Advance (CIA) Think on-line ordering. I place an order and pay for it now, you deliver it to me later. -> Technically this is a liability. If you fail to deliver the product, you owe me a refund. Most places actually treat this as cash.

Is this a payment AFTER delivery? Terms such as Net30. This actually goes against the Accounts Receivable, which may or may not be cash.

Does the payment involve late fees? Terms are Net30, customer pays in 45 days. The portion that goes for the product is A/R. The interest paid is something else. Some places just consider it all as cash.

Some places have partial payments, such as 30% CIA, 40% COD and 30% Net30. In which case, the payment would fall into any of the above categories.

Note: These comments are based on the CASH method of accounting. There is another, called the ACCRUAL method, which is normally for subscription services. If that is what you are using, the answers may be different.

This is the way we did accounting in my manufacturing company.

Hopefully, this post will give you enough information to discuss it intelligently with your controller to get the best answer for you and your company.
YMMV

Yes, undeposited checks are generally treated as cash since they are easily convertible to cash (and serve no other business purpose).

Bank statement reconciliation is typically separate from (but related to) financial accounting, so "cash" on the balance sheet may not exactly tie to the sum total of all bank accounts at any given time, due to both incoming and outgoing checks that have not fully cleared.

I would note, though, that if you maintain accrual accounting then it doesn't matter - you record revenue when the service is performed, not necessarily when you are paid.

If you use accrual accounting, you should treat the check as cash. When you sold the product, you probably sent your customer a bill. Under accrual accounting, you record revenue when you earn it. You earned the check as soon as you sold the product to your customer. Thus, you should have made the following journal entry: Debit Accounts Receivable and Credit Service Revenue. When you received the check, the journal entry should have been: Debit Cash and Credit Accounts Receivable. Thus, your check is the Debit to Cash.