Are Chinese language equivalent of English /p/ and /b/ sounds the same? As per my knowledge, both these sounds are considered the same in Mandarin. Do Chinese speakers them have difficulty in distinguishing between say Paul and Ball? How do they deal with it?
In the International Phonetic Alphabet, for stop consonants, the three following categories are distinguished:


(Truly) voiced stops. The vocalization begins before the release of the stop. Examples would be [b], [d], and [g]
Voiceless, unaspirated stops. The vocalization begins simultaneously with the release of the stop. Examples: [p], [t], [k].
Voiceless, aspirated stops. The vocalization begins shortly after the release of the stop. This is often perceived as a "puff of air". Examples: [pʰ], [tʰ], [kʰ].


The true situation is a little more complicated, but for any given language, we really only need to distinguish 2 or 3 of these in order to explain the phonological structure. To give some examples:


In English, our voiced stops (e.g., spelled "b", "d", and "g") are pronounced as voiced consonants; that is, [b], [d], and [g]. Our unvoiced stops are pronounced as either aspirated or unaspirated depending on context: "pop" = [pʰap], "stop" = [stap], and so forth.
In Mandarin, the distinction is between aspirated and unaspirated. There are no voiced stops at all: 白 = [pai], 拍 = [pʰai].
In many languages (including, say French), the distinction is between voiced and unvoiced, and there is no aspiration. So, you have "tout" = [tu], "deux" = [dœ].


The mismatch between different 2-way distinctions can either be unnoticable or a huge communication barrier. My experience is that English speakers have no problem communicating with either the aspiration-distinguishers or the voicing-distinguishers. If I say "to"/"do" (= [tʰu]/[du]), an aspiration distinguisher will perceive it as [tʰu]/[tu], and a voicing distinguisher will perceive it as [tu]/[du] (and vice versa).

The real problem is when aspiration-distinguishers attempt to communicate with voicing-distinguishers. This can be hard. A Chinese friend of mine complained about an Indian person who asked for "the [t]ime", and she had no idea what the "dime" he was asking about! Similarly, I've heard Europeans complain that Pinyin "makes no sense" because pinyin 'p' and 'b' "sound the same".

To address the OP's question, Mandarin speakers do distinguish a "p" and "b", but they do so on the basis of aspiration. This works fine for communicating with native English speakers, but works poorly for communicating with other non-native speakers who only make voicing distinctions (e.g., many Europeans).