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Dedicated hosting is where one customer has the whole PC to himself.
So the only real difference is that your website is being powered by a webserver which may be powering 15 or 20 (perhaps more) other websites.
Often, all those other websites will be on the same IP address as yours (which may or may not contribute to SE rank - I have read argument on here to suggest that a dedicated IP per website is better). But that in itself won't affect PageRank which is purely based on link structure. It's a link popularity score, that's all.
TJ