It depends on the complexity of the regex you're searching with. Regex engines usually build some sort of state machine from your regex, sort of like a compiler. Then they use that to check against the string. A state-machine based implementation will just be slower because of all of the extra variable changes it's having to do, but with simple enough regexes the compiled state machine might be fairly similar to this.
Regexes also aren't guaranteed to be much faster than a hand-written implementation for things like finding phone numbers, etc. They're pretty darn fast, don't get me wrong, but there might possibly be optimizations that could be made for specific use cases. Regex is just a convenient abstraction. Much like Javascript or Python, it's "just fast enough" for the vast majority of use cases, but for some like these, you need a better implementation for it to be performant.
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It depends on the complexity of the regex you're searching with. Regex engines usually build some sort of state machine from your regex, sort of like a compiler. Then they use that to check against the string. A state-machine based implementation will just be slower because of all of the extra variable changes it's having to do, but with simple enough regexes the compiled state machine might be fairly similar to this.
Regexes also aren't guaranteed to be much faster than a hand-written implementation for things like finding phone numbers, etc. They're pretty darn fast, don't get me wrong, but there might possibly be optimizations that could be made for specific use cases. Regex is just a convenient abstraction. Much like Javascript or Python, it's "just fast enough" for the vast majority of use cases, but for some like these, you need a better implementation for it to be performant.