Often, the recruiter has:
- a maximum of candidate that he is allowed to present set by his
customer, like 1 or 2
- a deadline
Depending of the negotiation between his agency and his customer, they may have a exclusivity period like 24H or 48H where the customer must accept or decline the candidates, after the deadline, other recruiting agencies may send candidature.
So multiple scenarios can happen ...
The recruiter sign you up, but another candidate look better, because the limit is 1, he present the other candidate and even if this candidate is declined, you are no more allowed to apply with another agency even if you were not presented.
Here another one:
The recruiter customer is a large known company. They have multiple departments and because they promote self management team, each department use the recruiting agency that fulfill their needs. You got a call from recruiter1 for a position in department1, later, you get a call from recruiter2 for department2 with the same generic position title at the same company but it is not the same position even if the job description match.
Scenario1 show there is a lot of trust with recruiters. You never know if they represent you or not and if everything they say is true: how they present their customer, the position, salary/rate expectation. I recommend to deal with the only one that you trust.
Scenario2 show there is a lot of job in the market, when you accept a recruiter represent you, I suggest to ask him to write down the ID of the position given by his customer in your contract/mail. This will allow you to be presented by two agencies for two different positions at the same customer.
At this point, I would I will forget about this role, getting represented by recruiter B may lead to legal dispute and if this happen, you need to be a super star or having rare skills in your field to not let be dropped by the customer.
You may ask some clarification from both recruiters to get a feel from them for the next opportunity. At first glance, I would not believe both recruiters because A seems to have lie while B seems to badmouth A and seems to gamble by pushing you to get represented twice at the same company which may get you in some troubles.