If they were the same people, the British might have said so, don't you think?
In the first report of the Mandatatory, the Palestinian population was described as:
" There are now in the whole of Palestine hardly 700,000 people, a population much less than that of the province of Gallilee alone in the time of Christ.* (*See Sir George Adam Smith "Historical Geography of the Holy Land", Chap. 20.) Of these 235,000 live in the larger towns, 465,000 in the smaller towns and villages. Four-fifths of the whole population are Moslems. A small proportion of these are Bedouin Arabs; the remainder, although they speak Arabic and are termed Arabs, are largely of mixed race. Some 77,000 of the population are Christians, in large majority belonging to the Orthodox Church, and speaking Arabic. The minority are members of the Latin or of the Uniate Greek Catholic Church, or--a small number--are Protestants.
The Jewish element of the population numbers 76,000. Almost all have entered Palestine during the last 40 years. Prior to 1850 there were in the country only a handful of Jews"
The Trans-Jordan population was described in the same report in the Trans-Jordania section of the report as:
"Trans-Jordania has a population of probably 350,000 people. It contains a few small towns and large areas of fertile land, producing excellent wheat and barley. The people are partly settled townsmen and agriculturists, partly wandering Bedouin; the latter, however, cultivate areas, more or less fixed, during certain seasons of the year."
Mandate for Palestine - Interim report of the Mandatory to the League of Nations Balfour Declaration text 30 July 1921
Why always the British, whe they were just lap dogs for the LoN.