Rails RSpec use mock instead of stub

Question

I've got a lib which deals with some external API. The details are irrelevant, everything works well:

module SampleApi
  extend self

  def fetch_mm_recommender(email:)
    handle_response(client.get("#{Sample.test_uri}/api/v1/mm_recommender", email: email))
  end

  private

  def handle_response(response)
    return parse_body(response) if response.success?

    Rails.logger.error "Request failed with code: #{response.status}, message: #{response.reason_phrase}"
    response.reason_phrase
  end

  def parse_body(response)
    JSON.parse(response.body)
  end

  def client
    @client ||= HttpHelper.new(with_cert: true)
  end
end

I've made RSpec test for that:

  describe '#fetch_mm_recommender' do
    subject(:fetch_physician) { described_class.fetch_mm_recommender(email: email) }

    let(:email) { '[email protected]' }

    context 'when email exists in SAMPLE' do
      before do
        stub_request(:get, %r{/api/v1/mm_recommender})
          .to_return(status: 200,
                     body: sample_response,
                     headers: {})
      end

      it 'fetch user data' do
        expect(fetch_physician).to be_present
        expect(fetch_physician).to eq(JSON.parse(sample_response))
      end
    end

Shouldn't I use mock rather than stub? Would there be any benefit to this? if so, what should such a test look like?

[EDIT]

context 'when email does not exist' do
  let(:email) { '[email protected]' }
  let(:sample_response) { 'Not found'.to_json }

  before do
    stub_request(:get, %r{/api/v1/mm_recommender})
      .to_return(status: 404,
                 body: sample_response,
                 headers: {})
    allow(Rails.logger).to receive(:error)
  end

  it 'does not retrieve data' do
    expect(fetch_physician).to eq('')
    expect(Rails.logger).to have_received(:error).with('Request failed with code: 404, message: ')
  end
end